Moment Generating Function for Binomial Distribution

The mean and the variance of a random variable X with a binomial probability distribution can be difficult to calculate directly. Although it can be clear what needs to be done in using the definition of the expected value of X and X2, the actual execution of these steps is a tricky juggling of algebra and summations. An alternate way to determine the mean and variance of a binomial distribution is to use the moment generating function for X. Binomial Random Variable Start with the random variable X and describe the probability distribution more specifically. Perform n independent Bernoulli trials, each of which has probability of success p and probability of failure 1 - p. Thus the probability mass function is f (x) C(n , x)px(1 – p)n - x Here the term C(n , x) denotes the number of combinations of n elements taken x at a time, and x can take the values 0, 1, 2, 3, . . ., n. Moment Generating Function Use this probability mass function to obtain the moment generating function of X: M(t) ÃŽ £x 0n etxC(n,x))px(1 – p)n - x. It becomes clear that you can combine the terms with exponent of x: M(t) ÃŽ £x 0n (pet)xC(n,x))(1 – p)n - x. Furthermore, by use of the binomial formula, the above expression is simply: M(t) [(1 – p) pet]n. Calculation of the Mean In order to find the mean and variance, youll need to know both M’(0) and M’’(0). Begin by calculating your derivatives, and then evaluate each of them at t 0. You will see that the first derivative of the moment generating function is: M’(t) n(pet)[(1 – p) pet]n - 1. From this, you can calculate the mean of the probability distribution. M(0) n(pe0)[(1 – p) pe0]n - 1 np. This matches the expression that we obtained directly from the definition of the mean. Calculation of the Variance The calculation of the variance is performed in a similar manner. First, differentiate the moment generating function again, and then we evaluate this derivative at t 0. Here youll see that M’’(t) n(n - 1)(pet)2[(1 – p) pet]n - 2 n(pet)[(1 – p) pet]n - 1. To calculate the variance of this random variable you need to find M’’(t). Here you have M’’(0) n(n - 1)p2 np. The variance ÏÆ'2 of your distribution is ÏÆ'2 M’’(0) – [M’(0)]2 n(n - 1)p2 np - (np)2 np(1 - p). Although this method is somewhat involved, it is not as complicated as calculating the mean and variance directly from the probability mass function.

Science and Technology in World Agriculture - 735 Words

In â€Å"Science and Technology in World Agriculture: Narratives and Discourses,† Pasquale Lucio Scandizzo persuades the experts in biotechnology that the World Bank can create a balance between conservative and radical parties. In order to reinforce his stance, Scandizzo uses various forms of evidence: the narratives of both parties, the description the ecological problems, and the World Development Report. Scandizzo uses a description of the narratives of both conservative and radical parties to establish common ground amongst readers. This evidence is important because he realizes that his readers might come from either one of those parties. Therefore, Scandizzo creates a balance by equally providing evidence of narratives from conservative and radical parties. Providing a balanced narrative for both views effectively shows readers that Scandizzo values the neutral position between two opposing views. This is important to successfully gain attention from both types of readers to continue listening to what Scandizzo is saying. In telling the evidence of narratives from both sides, Scandizzo is more concerned with discussing both sides’ achievements in increasing the yield in agriculture. This is effective because it creates a dynamic in readers’ minds: Scandizzo can first boost readers’ confidence about their belief and, in turn, makes readers consider the achievem ents of the opposite parties, thus successfully establishing common ground. Before Scandizzo describes theShow MoreRelatedTechnology And Farming During The World809 Words   |  4 PagesTechnology and Farming Introduction Many advances in farming have helped the world grow and prosper, for example, technology has changed farming drastically by enabling farm equipment to be motorized, allowing farmers to be able to farm more land and more crops, and by allowing scientists to experiment and make hybrid crops. 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Concepts Analyzing the ALDI Supermarket †MyAssignmenthelp.com

Question: Discuss about the Concepts Analyzing the ALDI Supermarket. Answer: Introduction ALDI Australia is regarded as one of the most discounted supermarkets that looks forward to offer products of greater quality at very low prices. The supermarket focuses on the exceptional value of the product having a greater quality. Their goal is to provide the customers grocery products of full range. A customer friendly supermarket enables the customer to shop in a smarter way (Aldi.com.au 2017). ALDI has expanded its branches and also brought structural changes in the organization. The aim of the topic is to apply a particular theory and concepts to describe the structural change. ALDI : Changes that took place in the organization ALDI has made a confirmation that more number of stores locations would open in the end of the year 2017. Initially in the year 2015, ALDI has expanded its branches in the other parts of Australia and also brought a change in the structural reforms by appointing a new Chief Executive Officer in the office. ALDI brought this structural change in terms of expansion in order to keep with the competitive advantages (Aldi.com.au 2017). With the increase of the new entrants in Australia, the rise of the consumers demands have become the important reasons to push the interest of the ALDI to expand its branches. The situation has permitted the organization to bring a structural change (Aldi.com.au 2017; Burke, 2017). Against this background, to relate the role of the manager has to be related with certain theories and concepts. The application of the PESTEL analysis and the description of the SWOT analysis in this topic, would enable the research to be done accordingly of the market structure. PESTLE analysis of ALDI Political analysis: The government of Australia might bring transformation if the new political parties are elected. However, the concern of multinational corporations is about the change in laws irrespective of the fact, which government is in the power. This in turn might affect the status quo of the ALDI Australia regarding the next decision the company takes. Economic analysis: The consumer expenditure includes the declining of GDP of Australia since the year 2003, the increasing level of the debt of the houses. However, the continuous fall in the levels of unemployment would lead to the enhancement of the purchasing power of the customers; this might lead to the increase of profit of the Australian supermarket. Sociological analysis: The Australian population is increasing, which might lead to the increase in the level of the consumers want. To top it, the huge migration from the South Asian countries, would led to the increase of the population in Australia. With the rise of consumer level in the country, the ALDI Australia derives economic benefits from the consumers by selling more items. Technological analysis: With the increasing use of internet, Australia is also connected with a fiber optic technology having the satellite coverage. The ALDI can easily reach the customers for their promotion of their products. Environmental analysis: The supermarkets of ALDI manage the carbon emission process. They take care of the fact that, the atmosphere is not getting polluted. Legal analysis: Australia follows the legal system of Common Law which is quite challenging to the ALDI since it is considered to be a German of Company and they are actually accustomed to the usages of the The Code Law (Yuksel 2012; Aldi.com.au 2017) SWOT analysis of ALDI Strengths: The ALDI claimed to have super quality products that they give in an affordable price. The shop looks forward to keep the cost of the operation low. It has the operation for over 15 countries in the world. Weaknesses: The ALDI supermarket is comparatively smaller. It has not impacted globally. However, it is at times considered to sell low quality at cheap prices. Opportunities: The super market needs to invest in advertisement in order to gain competitive advantages. It needs to grow its economy in Asia, Africa and in many other countries. Threat: The supermarket has engaged itself in the competition with retailers who have different Stock Keeping Units and the private level brands of the supermarket can get eclipsed by the other established brands (Hill, Jones and Schilling 2014; Aldi.com.au 2017). Conclusion On a concluding note, it could be stated that, ALDI supermarket is a growing market and the application of the contingency theory, Chaos theory and the SWOT concept helped to analyze the strategy of the organization. The application of these theories provided a basic understanding of the structure of the organization. References Aldi.com.au. 2017.ALDI Australia - ALDI Australia. [online] Available at: https://www.aldi.com.au/en/ [Accessed 19 Jul. 2017]. Hill, C.W., Jones, G.R. and Schilling, M.A., 2014. Strategic management: theory: an integrated approach. Cengage Learning. Yksel, ?., 2012. Developing a multi-criteria decision making model for PESTEL analysis.International Journal of Business and Management,7(24), p.52. Burke, W.W., 2017.Organization change: Theory and practice. Sage Publications.

Causes of Childhood Obesity Essay Example For Students

Causes of Childhood Obesity Essay Causes of Childhood Obesity Essay Works Cited Axmaker, Larry. Childhood Obesity Should be Taken Seriously. Online Posting 24 November 2004. Accessed 9 April 2005. 1-4. Bastin, Sandra. Perils of Childhood Obesity. American Academy of Pediatrics Quarterly. Volume 31 (11/2001): 44-49. Retrieved Medline 9 April 2005. 1-5. Buffington, Cynthia. Causes of Childhood Obesity. Beyond Change: Information Regarding Obesity and Obesity Surgery. Volume 17 (12/2003): 12-17. Retrieved Academic Search Elite 9 April 2005. Oklahoma Cooperative Extension Services. Special Issues: Childhood Obesity. Online Posting 7 July 2003. Accessed 9 April 2005. 1-5. Reading, Richard. Increasing prevalence of obesity in primary school children: cohort study. Child: Care, Health Development; Vol. 28 Issue 2 (03/2002): 189-197 Retrieved Academic Search Elite 9 April 2005 Rush, Traci. Childhood Obesity. Online posting 13 October 2002. Accessed 9 April 2005. 1. When speaking of her 8-year old daughters obesity, a prideful mother replies Oh its no big deal, she just still has her baby fat. Unfortunately, chances are that the daughters obesity is really no cause of her baby fat, but can be contributed to a combination of diet, genetics, and a sedentary lifestyle. Studies show that obesity among children 6-17 years of age, has increased by 50% in the last 20 years, with the most dramatic increase seen in children ages 6-11 (Axmaker, 1). This obvious epidemic has raised great concern in the medical community because widespread childhood obesity has increased the prevalence of the once rare juvenile diabetes and pediatric hypertension (Bastin, 45). This concern has prompted intense investigation of the causes of childhood studies, aside from socioeconomic status, three major causes have been shown: diet, genetics or biological factors, and lifestyle. Because fat must have a source from which to increase, diet is an obvious contributor to obesity in children. Dietary guidelines recommend that children between the ages of 6 and 11 should receive about 1800 calories a day, with 50% from carbohydrates, 30% from fat, and 20% from protein (Bastin, 47). With the ready availability of high calorie/high carbohydrate soft drinks, fruit juice, and high carbohydrate snacks, childrens diets have become increasingly less nutritious. Surveys conducted among children and teenagers have shown that 7 out of 10 children eat fruit once a day, and 5 out of 10 teenagers eat fruit once a day (Bastin, 47). Because children are replacing the missing fruit servings with high calorie snacks, weight gain will occur dramatically over time. An over consumption of 50-100 calories can lead to a gain of 5-10 pounds a year (Oklahoma Cooperative, 1). Many parents mistakenly encourage carbohydrates with a high-glycemic value as substitutes for fat and protein. High-glycemic carbohydrates prevent fat breakdown and drive fat into fat deposits, causing fat to accumulate, which occurring in high levels is obesity. The era of home cooking has all but disappeared from our society, with meals being replaced with pizza, or fast food creating yet another innutritious aspect of childrens diets. Carbohydrates also take far less time to empty from the stomach than do those foods high in fat or protein, causing hunger (Buffington, 14). A child having eaten a bowl of cereal for breakfast is likely to be hungry by mid-morning with the need for a snack. At school, he or she may satisfy their mid-morning hunger with yet another high carbohydrate food such as a soda, candy, cookies, or a bag of chips. These poor food choices are contributing to the increasing epidemic of childhood obesity. Everybody knows the child that can eat any type of food all day and never seem to gain weight. This occurrence has led researchers to investigate the role that genetics plays in childhood obesity. Not all children who are inactive or who eat poorly are obese, much in the same way that some obese children eat fairly healthy, and exercise moderately. Heredity has recently been shown to influence body fat percentage, regional fat storage, and the bodys response to overeating (Rush, 1). Children who have obese parents are 80% more likely to be obese than their lean parented counterparts (Buffington, 16). This familial correlation is contributed to genetics as well as the parents eating habits. History of Anthropology EssayResearchers suggest that a sedentary lifestyle is the greatest cause and predictor of childhood obesity (Bastin, 46). This sedentary lifestyle is due in large part to television, computers and video games occupying much of a childs time that would otherwise be spent in physical activities. Some studies have shown that children and teenagers spend up to 25 hours a week in front of the television, not including the time spent using computers or playing video games (Bastin, 46). With the increased time of television viewing, not only are childrens lifestyles becoming more sedate, but they are eating higher calorie foods in these drastically reduced times of activity. Researchers have found a very close correlation between Television viewing and the consumption of high calorie snacks (Oklahoma Cooperative, 3). When children combine extended periods of inactivity with consumption of high calorie snacks, a recipe for obesity is created. Studies conducted by t he American Academy of Pediatrics have shown that with every hour of television a child watches daily, chances of becoming obese increase by 2% (Bastin, 47). Years ago children typically spent this time outside engaging in physical activities. Not only did children get more exercise at home, but 80% of children were involved in physical education, while currently only 20% of children are involved in some type of physical education (Rush, 1). Educators hope to increase academic performance by decreasing emphasis on physical aspects of education, disregarding that recess fosters free and creative play, a component necessary for children to develop properly (Axmaker, 3). Much like in dietary respects, sedentary lifestyles can create a cycle in which, inactivity promotes obesity, and obesity promotes inactivity, making it difficult for a child to overcome obesity. Because of the drastic increase in obese children as well as adults, the issue of child obesity is finally being given the attention warranted. While many people may suggest that only one factor contributes to a childs obesity, scientists know that it is a conglomerate of factors all playing a role in whether or not a child will become obese. While diet and genetics play a large role, scientists are finding more and more that the factor with the greatest effect on obesity is a childs lifestyle. Childrens television viewing time should be limited, while active play should be encouraged. If parents and children alike can create a healthy balance between genetics, diet and lifestyle, the growing issue of obesity may one day be no longer a concern, and generations will live to be healthier.