How to Calculate the Variance of a Poisson Distribution

How to Calculate the Variance of a Poisson Distribution The variance of a distribution of a random variable is an important feature. This number indicates the spread of a distribution, and it is found by squaring the standard deviation. One commonly used discrete distribution is that of the Poisson distribution. We will see how to calculate the variance of the Poisson distribution with parameter ÃŽ ». The Poisson Distribution Poisson distributions are used when we have a continuum of some sort and are counting discrete changes within this continuum. This occurs when we consider the number of people who arrive at a movie ticket counter in the course of an hour, keep track of the number of cars traveling through an intersection with a four-way stop or count the number of flaws occurring in a length of wire. If we make a few clarifying assumptions in these scenarios, then these situations match the conditions for a Poisson process. We then say that the random variable, which counts the number of changes, has a Poisson distribution. The Poisson distribution actually refers to an infinite family of distributions. These distributions come equipped with a single parameter ÃŽ ». The parameter is a positive real number that is closely related to the expected number of changes observed in the continuum. Furthermore, we will see that this parameter is equal to not only the mean of the distribution but also the variance of the distribution. The probability mass function for a Poisson distribution is given by: f(x) (ÃŽ »x e-ÃŽ »)/x! In this expression, the letter e is a number and is the mathematical constant with a value approximately equal to 2.718281828. The variable x can be any nonnegative integer. Calculating the Variance To calculate the mean of a Poisson distribution, we use this distributions moment generating function. We see that: M( t ) E[etX] ÃŽ £ etXf( x) ÃŽ £etX ÃŽ »x e-ÃŽ »)/x! We now recall the Maclaurin series for eu. Since any derivative of the function eu is eu, all of these derivatives evaluated at zero give us 1. The result is the series eu ÃŽ £ un/n!. By use of the Maclaurin series for eu, we can express the moment generating function not as a series, but in a closed form. We combine all terms with the exponent of x. Thus M(t) eÃŽ »(et - 1). We now find the variance by taking the second derivative of M and evaluating this at zero. Since M’(t) ÃŽ »etM(t), we use the product rule to calculate the second derivative: M’’(t)ÃŽ »2e2tM’(t) ÃŽ »etM(t) We evaluate this at zero and find that M’’(0) ÃŽ »2 ÃŽ ». We then use the fact that M’(0) ÃŽ » to calculate the variance. Var(X) ÃŽ »2 ÃŽ » – (ÃŽ »)2 ÃŽ ». This shows that the parameter ÃŽ » is not only the mean of the Poisson distribution but is also its variance.

The Death Penalty Essay Example | Topics and Well Written Essays - 500 words

The Death Penalty - Essay Example There are many other countries that also adhere to the death penalty, though their practices of administering the death penalty differ from the United States, as well as what constitutes a death-worthy crime. Approximately twenty-five nations throughout the world believe in and practice the death penalty. Those that do not uphold any form of the death penalty find the actions to inhumane and lacking in ethic. Most of these nations, as well as the states in the United States that do not practice the death penalty, prefer to imprison their more hardened criminals for a lengthy amount of time with sentences that usually exceed life. I believe that the death penalty is not serving the purpose that it should. People are still committing violent crimes despite its existence. Furthermore, with the amount of exonerated deaths due to inconsistencies in the criminal justice system, the death penalty is proving to be more harmful than beneficial. Not only is the death penalty condoning the acti ons of those on death row, but it is bringing about the deaths of innocent people, which is yet another flaw in the death penalty.

Financial and monitoring strategy Essay Example | Topics and Well Written Essays - 750 words

Financial and monitoring strategy - Essay Example The new Office and Finance Manager has proposed the following financial and monitoring system with special attention to the legal and tax information requirements of ATO. As Real-time is registered for paying both GST and PAYG, the company is liable to maintain and provide records pertaining to tax calculations. These records should be kept for a minimum of 5 years as per legal requirements. As the company registered last year for payment of both these taxes, it is proposed that back up copies of accounting records and information listed as below to be kept in both hard copy forms as well as in soft copies written to CDs. As Real-time is currently having a computerized accounting system with customized business software, it is not a difficult task to acquire the necessary information and reports. However there is a marked lack of procedures for maintaining some of the above records and proof of information such as cheque stubs, deposit slips and credit card dockets. At most times, these items are discarded at month end or misplaced without being file and kept for record keeping. As such it is proposed that a record room be allocated separately for safekeeping or accruing records, bearing in mind the minimum five year requirement for maintaining business records to meet legal requirements. Investment in a low range server is also proposed so that the company’s computer system can be updated and all personnel be linked via network connections. This upgrading will also facilitate the implementation of the fleet tracking and monitoring software program proposed in a bid to minimize idle times, and other costs associated with ineffective delivery activities. As GST is payable on the service bills of Real-time, the GST component of 10% of bill value will be recorded in all invoices. The invoicing system has been already adjusted to carry out this task and the GST payable component is calculated automatically by

Discuss the History of Korea and Its Impact on Korea Essay Example for Free

Discuss the History of Korea and Its Impact on Korea Essay Topic: Discuss the history of Korea and its impact on Koreas culture, politics and business. Korea is a civilization and formerly unified nation currently divided into two states. Korean civilization is one of the oldest ancient civilizations in world history, and Korea has the oldest history in East Asia. * GoJoseon (National foundation in BC 2333) The first Korean kingdom GoJoseon was established on a flourishing bronze culture in BC 2333 by Dangun who was the legendary founder of Go]eseon and people believed he was the grandson of heaven (Edward 2005). It was centered in the basins of Liao China) and Northern part of the Korean Peninsula. Politics and economy In Korean history, GoJoseon was the first state to unify its political and religious functions within one governing system and legal system as represented by its Eight Prohibitions (Edward 2005). Society It is believed that GoJoseon had achieved the status of a kingdom with a class-based society. * Three Kingdoms penod ( BC 18 AD 676) Town-states gradually united into tribal leagues with complex political structures which eventually grew into kingdoms. Koguryo (BC 37 AD 668) Koguryo was the first to mature into a kingdom. Koguryds aggressive troops onquered neighboring tribes one after another, and in 313, they even occupied Chinas Lolang outposts (Qiancheng 2009). paekje (BC 18 AD 660) PaekJe, which grew out of a town-state located south of the Han River in the surroundings of present-day Seoul(Capital city of South Korea), was another contederate kingdom similar to Koguryo deane 2 Shilla (BC 57 AD 935) Shilla was the weakest and most underdeveloped among three kingdoms at the beginning. However, because it was geographically removed from Chinese influence, it was more open to non-Chinese practices and ideas. The society was built on an advanced Buddhist in Shilla (Edward 2005). unified Shilla (676-918) By the mid-sixth century, the Shilla kingdom had brought under its control all of surrounding town-states within the Gaya confederation. Through an alliance with China, Shilla finally unified the Korean peninsula in 668 and saw the peak of its power and prosperity in the mid-eighth century. It attempted to build an ideal Buddhist country during Unified Shilla but Buddhist social order started to deteriorate as the nobility indulged in increasing luxury (Kim 2005). Hwarang-do (Flower-knight art) in Unified Shilla It is culturally important to Korea and Taekwondo which is well known Korean martial arts in the world. It was a military academy for young, aristocratic youth in Unified Shilla. They intimated with nature and studied poetry, art, literature and song, as well as martial arts. Confucianism and Taoism also were very influential to Hwarang-do. The Hwarang-dds ethics and legends of this knighthood helped form the ethical background of taekwondo (Theodore 2005). * Koryo penod ( 918 1392) Internal dissensions and external problems of Shilla between the king and regional leaders led to the disruption of Shilla. The name Koryo derives from Koguryd and it is the root of the modern name of Korea. The Koryo period from 935 to 1392 was arked by periodic internal disharmony and external wars (mostly defensive) with China and Japan. And also Koryo was invaded by the Mongols in 1231 and Mongols nearly destroyed Koryo. However, there were also great achievements which are flowering of culture that led to great advances in art and scholarship, particularly in the ceramics industry, which developed the unique grey-green celadon stoneware for which Korea is well-known today (Thomas 2003). * Chosun Dynasty (1392 1910) In 1392, a general Yi Seong-gye founded a new dynasty Chosun. In the early Chosun period, Confucianism was highly supported as the guideline of philosophy. And then, this Confucianism transformed into Neo-confucianism incorporating Taoist and Buddhist elements with and adaptation of Confucianism. Neo-confucianism is what people know as Korean culture and tradition today (Thomas 2 From 1418 to 1450, by Chosuns fourth monarch king SeJong, Korea had an unprecedented flowering of art and culture. The greatest achievement of king SeJong was invention of the Korean alphabet Hangeul. Before he invented the Korean alphabet, Korean used Chinese character (Theodore 2005). In 1 592, Toyotomi Hideyosi, who united Japan, wanted to conquer the Korean Peninsula and use it the way for its incursion into China. However, Japan was defeated by Admiral Yi sun-sin, one of the most respected fgures in Korean history. They invaded again in 1597 but they withdrew in 1598. The new religion, Catholicism, slowly spread in Korea since 18th century by Dutch Jesuit priest. In the 19th century of Chosun, they adopted an isolationist policy by the prince Taewongun because he was afraid that Chosun would be infected by western ideas. Therefore, he tried to prevent the opening of the country to foreign trade by closing the borders (Edward 2005). * Korea under Japanese Rule (1910†1945) During Japanese occupation, the first thing they did was construction of Koreas nfrastructure especially street and railroad system to control all over Korea easily and supply food for Japanese military properly. Japanese ruled with iron hand and tried to root out all elements of Korean culture from society.

The Systematic Destruction of Womens Agency in Juárez, Mexico :: Gender Culture Murder Womens Agency Papers

The Systematic Destruction of Women's Agency in Juà ¡rez, Mexico As citizens, people rely on the state as an agent that acts on their behalf, by providing them with benefits such as basic protection. However, the state itself derives its power (or agency) from the fact that its citizens give up some of their individual agency in exchange for the benefits that belonging to a state provides. People are, thus, both the creators and the subjects of the state. In Juà ¡rez, Mexico the state has been shaped by a patriarchy that is very oppressive to women. The women are then subjects to this very oppressive state. Virginia Woolf claims that these women can gain agency and freedom by obtaining economic independence. But, in the case of Juà ¡rez, Mexico this economic freedom has deadly effects. Woolf's argument is very limiting and applied to a much more ideal situation. In this essay I will explore the climate in Juà ¡rez that seems to prove Woolf's theory wrong. I will also look at how her claims can offer hope to the women of Juà ¡rez so that they c an alter the climate so that everyone has agency not just the men and the state. Mexican culture has always placed the women in the home. Placement in the private sphere without the opportunity to earn money has always limited women's agency and freedom. Men have typically held the position of power because of their economic independence. As the holders of power in the public sphere, men have created a patriarchy in which the opinions have governed the laws that are passed within Mexico. Before the murders in Juà ¡rez began, and even still, women were offered very little protection by the government especially when it came to violence and rape. The machismo culture in Mexico sets up a climate in which young women can be beaten raped and murdered with little to no consequences. Domestic abuse laws in Mexico, state that a woman may not file domestic abuse charges if her wounds heal before the end of 15 days. Women are constricted to the private sphere according to Mexican culture. The women give up their rights to be in the public sphere with the hope and understa nding that they will be protected in the private sphere. They, however, do not receive this protection. Men can essentially beat their wives with no consequence. Additionally, rape laws are very lax.

How does Shakespeare present Ophelia Essay

In â€Å"Hamlet† Shakespeare presents Ophelia as a helpless girl, who is continually manipulated by the men around her for their own gain. In many of his other plays the women are presented as strong and admirable people who play major roles in the live of the protagonist, such as Lady Macbeth in â€Å"Macbeth. † In Hamlet, however, Ophelia becomes a very different role-she is conveyed as a lesser to the men around her. She is continually manipulated by her father, Polonius, her brother, Larertes and Hamlet, the supposed love of her life. Her sweet and innocent nature results in her becoming dependent on the man in her life to tell her how to behave. Hamlet shows a very different style in Shakespeare writing, no longer is the women controversially given respect by the male character, but is instead shown in a more traditional mere pawn for their fathers, brothers and lovers. Ophelia’s relationship with her father is less then the traditional intimate one expected. Instead it shows a controlling man, obsessed with what others think, and a daughter respectful of her fathers wises. Polonius becomes convinced that Ophelia’s relationship with Hamlet will result in the diminish of his families honour, and to him, the respect others have for his families reputation is very important. He thus begins to pressurise Ophelia into breaking off any understanding between herself and Hamlet. Shakespeare uses these characters and their interaction to present a more traditional view of how a woman should act toward the men in their lives during this time period. I personally do not see her as a week character, but instead see her as a women with no other choice than to respect and obey the man who has looked after her all her life. Their relationship is a cold one, with little compassion between the two, but apparent respect on Ophelia’s behalf. Her brother too becomes set against her love for Hamlet, believing that she will ruin herself for Hamlet, yet he will never actually marry her, due to her lower social standing. During the actual play, Larertes is the only man who conveys to her that he actually cares for her, but we can see clearly that he believes her continuous open regard for Hamlet will reduce their family’s nobility. He too adds to the pressure put on her to distance herself from Hamlet. Hamlets strategic plans towards Ophelia are probably the most conniving and vicious. He not only manipulates her constant love for him, but also toys with her emotions throughout, making her play exactly how he wants. He uses the courts knowledge of his relationship with Ophelia to get deeper involved in his plot to avenge his father and kill the king. He evolves Polonius’ theory that Hamlet is mad with love for Ophelia. When she returns Hamlets love letters and other tokens of his affections in act III scene I, Hamlet seizes this moment to cement the beginning of her descend into madness in both Ophelia’s eyes and in Polonius’ and Claudius’ as Hamlet is aware they are watching this encounter between the two ex-lovers. He appears troubled and hysterical as he denies giving her anything and laments the dishonesty of beauty. Confusingly, he claims to both have loved, and never loved her. As he leaves she mourns the â€Å"noble mind† that has now lapsed into apparent madness. Hamlet believes that by hearing this fight between Ophelia and himself, Polonius and Claudius will think he is now crazy and thus not fear him, making Claudius more vulnerable. Hamlet, Polonius and Larertes all put pressure on her to do what they want, they all use her to gain themselves and they all have little regard for her genuine love for Hamlet. Her heart begins to dictate over her head and as a result of being caught in the crossfire of all the men in her life; Ophelia goes crazy, unable to cope with the stress and contradiction. Finally, she kills herself finding no place in the situation for her own feelings. Hamlet is the least idealistic of Shakespeare’s plays, with women being presented in a more realistic view, rather than an idealistic outlook on society where women have more control over their lives and aren’t controlled by the men around them. Ophelia is presented in a more traditional feminine way, relying on men around her. This fits into Hamlet, and makes the play appear more legitimate, due to the emotion involved in the twisted love story. Still, I do not believe she is weak, but instead love struck and susceptible to manipulation by the men closely involved in her life. Many critics have argued that she is a dismal character, which no one can admire, but I see her as instead, a woman who is young, weak and naive to the world around her.

The Flu Vaccine and Community Health Free Essay Example, 2000 words

Literature review According to center for disease control and prevention (2009), the deaths associated with flu in America annually are approximately 300000 deaths. The figure is higher than deaths associated with cancer and HIV/AIDS. The figure is higher in the older population where 40% of the deaths occur on within patients of 65 years and above. The deaths and the number of resources invested in trying to prevent the deathly virus are high with it bearing the largest annual budget by the government and the health sector. The united state government pumps over three billion dollars annually towards managing the deadly virus. The costs are high as compared to other diseases. The deaths associated with influenza posse a major concern and the higher government expenditure is evident on how the virus has an impacting effect on the population. Vaccination among the health care workers The rate of infection is also high as compared to other diseases. The vaccine aims at reducing the infection to the health care personnel. The health personnel still poses a risk of infections, the center for disease and control (2003) indicate a passive nature of programs in initiating the vaccination program among the health care personnel. We will write a custom essay sample on The Flu Vaccine and Community Health or any topic specifically for you Only $17.96 $11.86/pageorder now It indicates the nature of failed mechanism to initiate the program with less than 40% of the entire population within the health sector being attainted. The most affected part is the voluntary practitioners who in most cases come in contact with the virus. The desired target is les attainable due to the initiated programs by the concerned party. According to Poland et al (2005) influenza outbreak in health facilities are on the decline but in the year 1998 an outbreak of influenza A was reported in one of the hospitals and after a survey only 12 % of the health care personnel in the hospital had been vaccinated against flu. The lack of vaccines on the health worker was the contributing factor of the spread and transmission of the Influenza A virus in the hospital. The transmission of the virus to the most vulnerable patients related to the low participant of health care personnel. Infection rates The infection of the virus among the enter population represents a 14% rate yearly. The different strain of the virus poses a threat to researcher in a bid to identify the needed vaccine for the aimed flu (Abate, 2014). The nature complicates the effort to identify the perfect vaccine per given interval. The continuous research to identify a universal vaccine has been fetal despite the heavy government involvement and funding.