Monday, May 25, 2020
This list of useful mobile apps for MBA students will help you create schedules, collaborate, network, improve productivity, and make the most of the MBA experience. iStudiez Pro iStudiez Pro is an award-winning multiplatform student planner that can be used to track class schedules, homework assignments, tasks, grades, and more. The app will notify you about important tasks and events so that you can get organized and stay on top of important deadlines and meetings. The iStudiez Pro app also offers two-way integration with Google Calendar and other calendar apps so that you can share schedules with classmates, members of your study group, or people in your social circle. Free cloud sync is available as well, making it easy to wirelessly sync app data across multiple devices. The iStudiez Pro app is available for: iOSmacOSAndroidWindows *Note: If you would like to try this app before you purchase it, a free version of the app, known as iStudiez LITE, is available through the App Store for iOS devices. Trello Millions of people - from small start-up businesses to Fortune 500 companies - use the Trello app to collaborate on team projects. This app works well for MBA cohorts and study groups who are collaborating on a project for a class or competition. Trello is like a real-time, virtual whiteboard that everyone on the team has access to. It can be used to create checklists, share files, and have discussions about project details. Trello can be synced across all devices and works with all major browsers so that you can access the app data wherever you are. The free version would work for most student groups and teams, but there is also a paid version for users who want special features, such as extra storage space or the ability to integrate data with an unlimited number of apps.Ã The Trello app is available for: iOSmacOSAndroidWindows Shapr Shapr is a professional networking app that is designed to make the entire process of networking less painful and time consuming. Unlike most networking apps, Shapr uses an algorithm that considers your tagged interests and location to connect you with like-minded professionals who are in your area and looking to network. As with the Tinder or Grindr dating apps, Shapr allows you to swipe right anonymously. The app will notify you when the interest is mutual so that you donÃ¢â¬â¢t have to deal with random, unsolicited requests to talk or meet up. Another plus is that Shapr presents you with 10 to 15 different profiles each day; if you donÃ¢â¬â¢t feel like you can connect with the people it shows you one day, there will be a fresh crop of options the following day. The Shapr app is available for: iOSAndroid Forest The Forest app is a useful mobile app for people who are easily distracted by their phone when they should be studying, working, or doing something else. When you want to focus on something, you open the app and plant a virtual tree. If you close the app and use your phone for something else, the tree will die. If you stay off your phone for the designated amount of time, the tree will live and become part of a virtual forest. But it isnt just a virtual tree at stake. When you stay off your phone, you also earn credits. These credits can then be spent on real trees that are planted by a real tree planting organization that has teamed up with the makers of the Forest app. The Forest app is available for: iOSAndroid Mindfulness The Mindfulness app is a useful mobile app for MBA students who are feeling overwhelmed or stressed out over school obligations. This app is designed to help people manage their mental health and well being through meditation. With the Mindfulness app, you can create timed meditation sessions that are as short as three minutes long or as lengthy as 30 minutes long. The app also includes nature sounds and aÃ dashboard that displays your meditation statistics. You can get the free version of Mindfulness or you can pay for a subscription to get additional features likeÃ themed meditations (calm, focus, inner strength, etc.)Ã and access to meditation courses.Ã The Mindfulness app is available for: iOSAndroid
Thursday, May 14, 2020
Why did Judge Hall choose John Jameson for CeliaÃ¢â¬â¢s defense? Given the impact of the slavery issue upon MissouriÃ¢â¬â¢s politics at the time, the Judge Hall hoped for the trail to be conducted as expeditiously and decorously as possible, in a manner that ran the least risk of arousing the ire of either camp. Judge Hall needed a capable attorney, one of considerable standing in the community. He needed an attorney with proven political sensibilities, one who had not participated significantly in the slavery debates. In short, he needed an attorney who could be depended upon to give Celia a credible defense, one whose presence would make it difficult for slaveryÃ¢â¬â¢s critics to label the trial a farce or sham and one who would not arouse theÃ¢â¬ ¦show more contentÃ¢â¬ ¦Hardly more than a month following Lincolns victory came declarations of secession by South Carolina and other states, which were rejected as illegal by outgoing President James Buchanan and President-elect Lincoln. The election of Lincoln in November 1860 was the final trigger for secession. Efforts at compromise, including the Corwin Amendment and the Crittenden Compromise, failed. Southern leaders feared that Lincoln would stop the expansion of slavery and put it on a course toward extinction. The slave states, which had already become a minority in the House of Representatives, were now facing a future as a perpetual minority in the Senate and Electoral College against an increasingly powerful North. Before Lincoln took office in March 1861, seven slave states had declared their secession and joined together to form the Confederacy. 1. West expansion 2. State rights 3. Economics 4. Irrepressible conflict 5. Slavery Causes of secession The Abolitionist movement in the United States had roots in the Declaration of Independence. Slavery was banned in the Northwest Territory with the Northwest Ordinance of 1787. By 1804 all the Northern states had passed laws to gradually abolish slavery. Congress banned the African slave-trade in 1808, although slavery grew in new states in the deep south. The Union was divided along
Wednesday, May 6, 2020
In today s society people have to deal with several issues that we can t explain. For some of us we built fences to isolate ourselves from others or in some cases to protect ourselves. No matter what the issue is we, all have to struggle to be able to provide for our families. As a child I built fences when it came to my feelings. For example, growing up I was in the chunky side. Since I wasnt so skinny like the pretty girls in my class. I kinda isolated my self from the other students. That way my feelings wouldn t get hurt. My fence was to protect me from what I thought was going to hurt me. Well the same thing happened to Troy Maxson. In the play, Fences written by the well-known playwright, August Wilson, is the story of Troy Maxson and his beloved family. Throughout the whole entire play, a fence is being built around the Maxson household. As the story unfolds to the viewers, the word fences may look like a simple title, but the truth is it has different symbolic meaning. The r eal definition of the word fence is revealed along with the personalities of the characters in the play. In Fences, August Wilson uses different types of fences as a metaphor to explain how these people live. Our play takes place during the year 1957. During the mid-1950s, America was still experiencing a post-World War II, economic boom, and of course allowing foreign affairs to take action when dealing with domestic issues. According to PBS channel during the year 1954 the SupremeShow MoreRelatedAnalysis Of August Wilson s Fence 1146 Words Ã |Ã 5 PagesLong Eng 200 August 13,2017 The play Ã¢â¬Å"FenceÃ¢â¬ by August WilsonÃ¢â¬â¢s has a connection with real world fence. Ã¢â¬Å"The yard is a small dirt yard, partially fenced, except for the last scene, with a wooden sawhorse, a pile of lumber, and other fence-building equipment set off to the side. The Opposite is a tree from which hangs a ball made of rags. A baseball bat leans against the tree. Two oil drums serve as garbage receptacles and sit near the house at right to complete the settingÃ¢â¬ (Wilson 2). He mentionsRead MoreAnalysis Of August Wilson s Fences1609 Words Ã |Ã 7 PagesIn 1965, August WilsonÃ¢â¬â¢s Ã¢â¬Å"FencesÃ¢â¬ was created as the fifth part of his Pittsburg Cycle of dramas of the 20th Century investigation of the evolution of black culture. The play has an abundance of symbolism and metaphors that tells the late life story of Troy Maxon and the family that surrounds him. Even from the beginning of the drama there is conflict and foreshadowing that can be attributed to his ow n belief that he has failed in life and that the world did not give him what he deserved. He takesRead MoreAnalysis Of August Wilson s Fences 970 Words Ã |Ã 4 PagesWe sometimes believe that by creating barriers around ourselves and the people we love, it will keep us safe and together. August Wilson is an African-American playwright from Pittsburg, Pennsylvania who was raised with his five brothers and sisters by his mother who worked hard to support them after his father, a white man left them. His mother found another man who also helped her raise them. In this time, it was very hard for African-Americans because it was the time when White Americans and AfricanRead MoreAn Analysis Of Henrik Ibsen s A Doll House And August Wilson Fences 1224 Words Ã |Ã 5 PagesTwo Women and Their Breaking Points Taking a glance at the work of Henrik Ibsen Ã¢â¬Å"A Doll HouseÃ¢â¬ and August Wilson Ã¢â¬Å"FencesÃ¢â¬ , readers would believe that the writerÃ¢â¬â¢s characters Rose and Nora could not be any more different from one another. But, as one would exceed deeper into the critical themes of the characters and of the two plays, the similarities can be drawn. The two women share more in common than ones may think, in terms of their characterization. In the play Ã¢â¬Å"A Doll HouseÃ¢â¬ the main characterRead MoreSymbolism In Fences By August Wilson1460 Words Ã |Ã 6 PagesKeep Love in or Lock it Out?: An Analysis of Symbolism in Fences Symbolism is defined as an artistic and poetic movement or style using symbolic images and indirect suggestion to express mystical ideas, emotions, and states of mind. In Fences by August Wilson, symbolism is used heavily throughout the play in order to represent deeper meanings and add to the emotion of the storyline. In order for the play to have so much depth and emotion, symbolism is crucial to the work itself and the heavy topicsRead MoreNotes On The Novel Fences And Pied Piper Of Tucson 1080 Words Ã |Ã 5 PagesYou Been?Ã¢â¬ and Mara BovsunÃ¢â¬â¢s article, Ã¢â¬Å"Pied Piper of Tucson;Ã¢â¬ they identify and describe ways authors Ã¢â¬Ëhook and holdÃ¢â¬â¢ readers with specific choices. Next, students read the play Fences by Pulitzer Prize winner August Wilson and analyze the role of stories within in the story to create tension and advance the plot. Fences is the foundation for the unitÃ¢â¬â¢s cornerstone task: after ranking and discussing important lines in the play, student perform them, and reflect on the impact of the important linesRead MoreFences Research1694 Words Ã |Ã 7 PagesBoundaries in August WilsonÃ¢â¬â¢s Fences The early 1950Ã¢â¬â¢s was a time of enormous importance because of the Civil Rights Movement which emphasized equal rights for blacks and whites. According to the book Approaching Literature, this time period became very familiar to August Wilson, the author of the play Fences. Wilson, an African American man, was raised by his mother and his ex-convict father. For a short period of time, before moving back to his old neighborhood, Wilson lived in a primarilyRead MoreSocial, Political, And Family Issues On August Wilson s Fences1596 Words Ã |Ã 7 PagesSocial, Political, and Family Issues in August WilsonÃ¢â¬â¢s Fences August WilsonÃ¢â¬â¢s Fences depicts life in the 1950s for a typical African American family. The play touches upon racism, shifting family dynamics, and the politics of war. While racism plays an important and vital role in the play, instead of lamenting the issue, Wilson uses the characters as a weapon against the rampant racism of the time. In the same fashion, the relationship between Troy, Rose, and Cory demonstrates the shifting culturalRead MoreFences: White People and Troy Essay1719 Words Ã |Ã 7 PagesAnalysis of Ã¢â¬Å"FencesÃ¢â¬ August WilsonÃ¢â¬â¢s famous play Ã¢â¬Å"FencesÃ¢â¬ is a drama set in the 1950Ã¢â¬â¢s. Being a winner of the Pulitzer Prize for the best play of the year, this play has had many positive responses to blacks and whites in this society. It is about protagonist Troy Maxson as well as his african american family that is filled with drama and excitement. In WilsonÃ¢â¬â¢s Fences by Joseph Wessling he expresses, Ã¢â¬Å"Fences is about the always imperfect quest for true manhood. TroyÃ¢â¬â¢s father was less of a Ã¢â¬Å"trueÃ¢â¬ Read MoreThe Rise And Fall Of Troy Maxon1278 Words Ã |Ã 6 PagesFall of Troy Maxon: An Analysis of August WilsonÃ¢â¬â¢s play Fences In Fences, August Wilson, the playwright, provides a believable and powerful examination of the African American experience in the late 1950Ã¢â¬â¢s. It provides an apt portrayal of the mentality of African American men going into the civil rights movement, as well as a well-developed account of the friction that occurs between a father and a son, and a husband and wife in the face of conflict. According to Wilson, his play provides Caucasians
Tuesday, May 5, 2020
Question: Write about theBenefits a Family Strengths Assessment for Family. Answer: Australian Family Strengths Nursing Assessment Guide contains nine components which are: affection, acceptance, togetherness, support, communication, commitment, resilience, sharing activities and spiritual well-being (Smith Ford 2013, Table 5.1, pp. 101-102); also, depends on the qualities based care idea where the nurse enables the patient and family to get solutions (Gottlieb 2013). The Australian Family Strengths Nursing Assessment Guide (AFSNAG) is useful in that it allows the medical attendant to animate a discussion with the patient and family over each of the segments (Smith and Ford 2013). Each of the characteristics of family qualities gives the nurse who is directing the evaluation with a more clear comprehension of the way a family works (Smith and Ford 2013); it reveals how a wellbeing condition is influencing the distinctive relatives and features their individual needs (Smith and Ford 2013). Albeit every family is novel and has their particular traditions, qualities and convictions, the AFSNA questions have been skillfully created and are open-ended; they are composed in a way that incorporates the entire family (Smith and Ford 2013). For instance, 'When does the family get to know each other?' (Smith and Ford 2013, pp. 101) or, 'What diverse obligations do each of you have?' (Smith and Ford 2013, pp. 101). It enables the relatives to recount their story in their own particular words and the way they see things. A huge advantage of the inquiries is that they can be adjusted to suit the conditions of the patient or potentially their family (Power, 2003). Every individual is influenced by a circumstance unexpectedly, especially when an impromptu emergency happens that they are not ready. From listening to the family's story, the nurse acquires a superior knowledge into the household and can watch how each of the relatives adapts (Gottlieb 2013). Recognizing the family's qualities and seeing how the family adapts is worthwhile to both the medical attendant and the family since changes in the way the family capacities can be started to expand their versatility (Patterson, referred to in Smith and Ford 2013). Enlisted nurses in Australia who have utilized the AFSNA tool in their clinical practice have lauded it (Smith and Ford 2013, p. 103). One nurse commented that it was 'reviving' to investigate the positive qualities of an individual and additionally their family as opposed to concentrating on the negatives (Smith and Ford 2013, p. 103). The nurse explained more on the advantages of the device expressing that it empowered families to solve problems by building up their qualities and objectives (Barnes et al. (n.d.). After the nurse has finished the appraisal, they can utilize the data accumulated from the patient and family to start setting up a care arrange for that meets the family's specific needs. The family will likewise have profited from being effectively associated with their particular social insurance and have their voices heard. Smith and Ford (2013) see the intelligent discussions between the nurse and the family as used because it advances 'ideal formative wellbeing and prosperity for each other' (Smith and Ford 2013, p. 102). References Barnes, M., Rowe, J., Smith, LM. Ford, K. (n.d.). Family strengths and the Australian Family Strengths Nursing Assessment Guide. Elsevier. Gottlieb, L. (2013). Strengths-based nursing care: health and healing for person and family. New York, Springer Publishing Company. Power, T. J. (2003). Promoting children's health: integrating school, family, and community. New York, Guilford Press. Smith, LM. Ford, K (2013). Conducting a family strengths assessment using the Australian Family Strengths nursing assessment guide. University of Tasmania.
Saturday, April 11, 2020
Correlation to AlthusserÃ¢â¬â¢s connection to structuralism When examining the illogical nature of ChinaÃ¢â¬â¢s construction industry, it bears a great deal of similarity to AlthusserÃ¢â¬â¢s connection to structuralism wherein he states that there are overarching socio-economic and ideological structures that ultimately have power to determine the other elements of the system, even though these other elements have a fair degree of autonomy.Advertising We will write a custom research paper sample on Chinese Real Estate Market specifically for you for only $16.05 $11/page Learn More In this particular case, it can clearly be seen that there is an overarching system in the form of the state capitalist based economic model of China that has influenced its government to such an extent that it pursued a path of real estate development that focused on creating high value properties. Since real estate development is normally an independent and autonomous s ystem that is based on consumer demand, the fact that real estate developers in China still adamantly pursues high end development despite lack luster demand is indicative of a structural system in place that dictates their actions. Evidence of this can be seen when examining regional wage developments within China (Sujian, 207-224). It was noted that the average salary of an ordinary Chinese worker is roughly 2,000 to 4,000 Yuan per month, which when converted utilizing the current monetary value of the British pound is equivalent to 190 and 380 pounds respectively or $270 and $520. While the wage can still relatively low, it is still considered by the Chinese government as an adequate level of monetary compensation for a bare minimum standard of living. An examination of average property prices for affordable housing within China done by Bradsher (2013) reveals that the average median home price within the country is equivalent to $114,900 The pricing situation present in ChinaÃ¢â ¬â¢s cities is roughly equivalent to average prices within western countries such as the U.S. yet the wage demographics within China is 6 times lower making most housing within the country unattainable by the average worker. What this shows is a failure on the part of a overarching structuralist system that attempted to grow based on a particular predetermined path yet failed spectacularly due to limited vision regarding the ramifications of its actions. ChinaÃ¢â¬â¢s Real Estate Market Within the past 2 decades ChinaÃ¢â¬â¢s economy has grown to become the second largest economy in the world as a direct result of government initiatives into encouraging foreign direct investment, local entrepreneurship and real estate development (Hui, 951-961).Advertising Looking for research paper on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More Unfortunately, as noted by studies such as Ã¢â¬Å"Study On China Real Estate Price Bub ble: Will It Burst Soon? (2011)Ã¢â¬ , though there may be a high rate of property development occurring within ChinaÃ¢â¬â¢s cities there is an increasingly prevalent rate of housing surplus within the country with well over 70 million surplus housing units expected to reach completion by the end of 2013. As stated by Shen (2009), ordinarily having a certain level of housing surplus would be fine if such housing initiatives were created in order to meet expected demand within the near future, however, Shen (2009) determined that property development within China is not concentrating on either affordable housing or subsidized housing schemes which are in great demand within China. Instead, what is present is a development strategy that is oriented towards high end property development. In fact, studies such as those by Hui (2012) which examined the 70 million housing surplus units within China took note of the fact that most if not all if these units had price schemes that were we ll above what an average Chinese worker would be able to afford. This presents a rather unusual situation since real estate construction within certain areas should reflect consumer demand which is not occurring within this particular case. Instead, what is occurring in the case of China is the complete opposite of what analysts say should be an ideal rate of local real estate development (Shen, 3). Understanding the Chinese Real Estate Market ChinaÃ¢â¬â¢s real estate market essentially works under 5 distinct forces that influence the development of its local real estate market. These forces are composed of: the central government, local government, banks, developers and consumers (Bradsher, 2). These particular 5 forces are ubiquitous in real estate markets around the world, yet, what makes the case of China unique is the greater degree of government control over the rate of development (Real Estate Bubbles and the National PeopleÃ¢â¬â¢s Congress, 20). This aspect of control wa s seen during the period of 2000 to 2008 where the central government effectively dictated the rate of real estate development within the country instead of allowing natural market forces such as demand and supply to influence the actions of developers (Shen, 18). This particular strategy was noted by Bradsher (2013) as being related to the central governmentÃ¢â¬â¢s desire to meet ever increasing GDP targets and, as such, utilized the real estate market in order to artificially drive up growth. The process of real estate development within China operates under the process of local government officials selling land to developers who build mainly 3 types of housing: subsidized housing for the poor, affordable housing for people with average incomes and high end residential properties (Study On China Real Estate Price Bubble: Will It Burst Soon?, 27).Advertising We will write a custom research paper sample on Chinese Real Estate Market specifically for you for only $16 .05 $11/page Learn More In the case of China, property auctions are often won by developers who chose to build high end properties due to the assumption that the cost of the land can be recouped through selling expensive housing units. It is mentioned by Fung and Yu (2011) in their examination of localized property development that it is not that high end property developers do not win land bids in various international real estate markets but rather it is often the case that high end property developers do not bid as often compared to subsidized housing or affordable housing developers. In the case of China, what is present is a high degree of demand for subsidized or affordable housing with a relatively low degree of demand for high end real estate yet what is present is a situation where there are more high end residential construction projects despite low market demand for that particular type of housing (Sujian, 207-224). Raymond Williams and Hegemony When examin ing the context of Raymond Williams and Hegemony, it can be seen that it is applicable to the case of China wherein an overriding Ã¢â¬Å"world viewÃ¢â¬ or Ã¢â¬Å"class outlookÃ¢â¬ influences the development of systems of belief within a particular country (Williams 108-114). While China may espouse that its brand of communism is Ã¢â¬Å"for the peopleÃ¢â¬ the fact remains that it is the political elite and rich that in effect dictate social and economic development within the region. ChinaÃ¢â¬â¢s real estate industry is an excellent example of domination and subordination in action. The rate of development that focuses primarily on high end real estate development in what can only be described as a form of Ã¢â¬Å"tunnel visionÃ¢â¬ focuses on the development of structures that appeal to the rich and political elite despite the lack of localized demand. As it has been mentioned before, in most systems, supply is meant to meet demand, however, when throwing in the concept of Williams and Hegemony into the mix, what occurs is that despite the lack of demand local corporations continue to supply since the focus is in conforming to the plan of the government for urban development despite the potential negative economic ramifications. This is one of the issues when it comes to state owned developers and hegemony wherein an overriding directive becomes the focus which causes problems for those that are being subordinated yet benefit those who dominate the system.Advertising Looking for research paper on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More State Influence in Local Real Estate Development As noted by Fung and Yu (2011) in their examination of real estate development within China, it was noted that one unique aspect of the Chinese banking sector was that most banks within China are actually controlled by the state as opposed to the situation in other countries where banks are not directly controlled by the government (Fung, Esther, and Yu, 5). This presents itself as a unique situation as described by the article Ã¢â¬Å"Restless (1998)Ã¢â¬ since this actually enables the central government to dictate lending rates, who to lend to and for what purpose (Restless, 3). As noted by Fontevecchia (2011), state owned companies tend to receive more preferential treatment from state owned banks (nearly all the banks in China are owned by the government) which in turn enables state owned companies to outbid private developers for land deals. In fact it has been noted by Bradsher (2013) and other similar studies that all around China state run corporations ranging from military, telecom to even oil producers have been venturing into the real estate development industry with which they utilize preferential treatment from banks to overtake private developers in the sheer amount of construction projects created. This has created a situation where multiple state run companies are investing into a platform that simply is not in demand which will result in an eventual catastrophe for the country. Works Cited Bradsher, Keith. Ã¢â¬Å"ChinaÃ¢â¬â¢s Central Bank Has Its Own Worries.Ã¢â¬ New York Times 29 May 2013: B2. Regional Business News. Web. Fontevecchia, Agustino. Ã¢â¬Å"China: When Falling Home Prices Are A Good Thing.Ã¢â¬ ForbesÃ (2011): 3. Print Fung, Esther, and Rose Yu. Ã¢â¬Å"Fitch Sees Bank Risks For China.Ã¢â¬ Wall Street Journal Ã¢â¬âÃ Eastern Edition Sept. 2011: C5. Business Source Premier. Web. Hui, Eddie Chi-Man, et al. Ã¢â¬Å"Real Estate Bubbles In China: A Tale Of Two Cities.Ã¢â ¬ Ã Construction Management Economics 30.11 (2012): 951-961. Print Ã¢â¬Å"Real Estate Bubbles And The National PeopleÃ¢â¬â¢s Congress.Ã¢â¬ Stratfor Analysis (2010): 20. Print Ã¢â¬Å"Restless.Ã¢â¬ Business China 24.24 (1998): 3. Business Source Premier. Web. Shen, Irene. Ã¢â¬Å"ChinaÃ¢â¬â¢s Premier Pledges To Control Real Estate Bubble, Holds Firm On Yuan.Ã¢â¬ Businessweek (2009): 18. Print Ã¢â¬Å"Study On China Real Estate Price Bubble: Will It Burst Soon?.Ã¢â¬ Allied AcademiesÃ International Conference: Proceedings Of The Academy For Studies InÃ International Business (ASIB) 11.1 (2011): 27. Print This research paper on Chinese Real Estate Market was written and submitted by user R0bert to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.
Tuesday, March 10, 2020
Expected Value of a Binomial Distribution Binomial distributions are an important class of discrete probability distributions. These types of distributions are a series of n independent Bernoulli trials, each of which has a constant probability p of success. As with any probability distribution we would like to know what its mean or center is. For this we are really asking, Ã¢â¬Å"What is the expected value of the binomial distribution?Ã¢â¬ Intuition vs. Proof If we carefully think about a binomial distribution, it is not difficult to determine that the expected value of this type of probability distribution is np. For a few quick examples of this, consider the following: If we toss 100 coins, and X is the number of heads, the expected value of X is 50 (1/2)100.If we are taking a multiple choice test with 20 questions and each question has four choices (only one of which is correct), then guessing randomly would mean that we would only expect to get (1/4)20 5 questions correct. In both of these examples we see thatÃ E[ X ] n p. Two cases is hardly enough to reach a conclusion. Although intuition is a good tool to guide us, it is not enough to form a mathematical argument and to prove that something is true. How do we prove definitively that the expected value of this distribution is indeed np? From the definition of expected value and the probability mass function for the binomial distribution of n trials of probability of success p, we can demonstrate that our intuition matches with the fruits of mathematical rigor. We need to be somewhat careful in our work and nimble in our manipulations of the binomial coefficient that is given by the formula for combinations. We begin by using the formula: E[ X ] Ã £ x0n x C(n, x)px(1-p)n Ã¢â¬â x. Since each term of the summation is multiplied by x, the value of the term corresponding to x 0 will be 0, and so we can actually write: E[ X ] Ã £ x 1n x C(n , x) p x (1 Ã¢â¬â p) n Ã¢â¬â x . By manipulating the factorials involved in the expression for C(n, x) we can rewrite x C(n, x) n C(n Ã¢â¬â 1, x Ã¢â¬â 1). This is true because: x C(n, x) x n!/(x!(n Ã¢â¬â x)!) n!/((x Ã¢â¬â 1)!(n Ã¢â¬â x)!) n(n Ã¢â¬â 1)!/((x Ã¢â¬â 1)!((n Ã¢â¬â 1) Ã¢â¬â (x Ã¢â¬â 1))!) n C(n Ã¢â¬â 1, x Ã¢â¬â 1). It follows that: E[ X ] Ã £ x 1n n C(n Ã¢â¬â 1, x Ã¢â¬â 1) p x (1 Ã¢â¬â p) n Ã¢â¬â x . We factor out the n and one p from the above expression: E[ X ] np Ã £ x 1n C(n Ã¢â¬â 1, x Ã¢â¬â 1) p x Ã¢â¬â 1 (1 Ã¢â¬â p) (n Ã¢â¬â 1) - (x Ã¢â¬â 1) . A change of variables r x Ã¢â¬â 1 gives us: E[ X ] np Ã £ r 0n Ã¢â¬â 1 C(n Ã¢â¬â 1, r) p r (1 Ã¢â¬â p) (n Ã¢â¬â 1) - r . By the binomial formula, (x y)k Ã £ r 0 kC( k, r)xr yk Ã¢â¬â r the summation above can be rewritten: E[ X ] (np) (p (1 Ã¢â¬â p))n Ã¢â¬â 1 np. The above argument has taken us a long way. From beginning only with the definition of expected value and probability mass function for a binomial distribution, we have proved that what our intuition told us. The expected value of the binomial distribution B( n, p) is n p.
Saturday, February 22, 2020
CHROMATOGRAPHY (ANALISIS CHEMISTRY) Coursework Example | Topics and Well Written Essays - 1000 words
CHROMATOGRAPHY (ANALISIS CHEMISTRY) - Coursework Example In thin layer chromatography, a thin, uniform layer of silica or alumina gel was traditionally coated on a piece of glass. The mixture was dissolved in an appropriate solvent and the glass plate was immersed in the liquid. The movement of the individual components of a mixture takes place at different rates and the distance travelled by each component is measured and the data so obtained is used to calculate the Rf value is calculated by dividing the distance travelled by the component with the distance travelled by the solvent. Rf values are then compared with standard values to identify the suspected component. Fluorescent materials are incorporated into the stationary phase to identify colorless components which are invisible to the naked eye. Such components are visualized using ultra violet light. Separation of components of a mixture depends upon their affinity for the solvent as well as the capability of bonding with the stationary phase which is rich in hydroxyl groups. Van d er Waals forces also operate between the components and their affinity or repulsion from the stationary phase and determine the distance moved. Column chromatography was advancement in the technique where the stationary phase was packed inside a column (glass tube) and the mobile phase with the dissolved investigative mixture poured from the top. The movement occurred under the influence of gravity as well as the attraction of the components in the stationary phase, allowing identification of individual components. HPLC (High Performance Liquid Chromatography/High Pressure Liquid Chromatography) is a modern technique used to separate desirable or investigative chemical compounds from other compounds in a liquid sample. The investigative compounds are dissolved in an appropriate organic or inorganic solvent known as the mobile phase and the mixture is passed under pressure through specific columns which constitute the stationary phase.