properties of a probability distribution To compute the expected value and variance of a probability distribution To calculate the covariance and understand its use in finance To compute probabilities from binomial‚ hypergeometric‚ and Poisson distributions How to use the binomial‚ hypergeometric‚ and Poisson distributions to solve business problems Copyright ©2012 Pearson Education‚ Inc. publishing as Prentice Hall Chap 5-2 Definitions Random Variables A random variable represents
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Triangle The Pascal’s Triangle is a triangular array of the binomial coefficients. The system after French mathematician Blaise Pascal. The set of numbers that form Pascal’s triangle were known before Pascal. However‚ Pascal developed many uses of it and was the first one to organize all the information together in his treatise‚ Traité du triangle arithmétique (1653). The numbers originally arose from Hindu studies of combinatorics and binomial numbers and the Greeks’ study of figurate numbers. The
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invented the binomial coefficients which are now known as Pascal’s Triangle. Pascal’s major input to the philosophy of mathematics came with his “Of the Geometric Spirit””.1 Blaise Pascal was also a major contributor to the founding of Statistics. Blaise Pascal contributed to mathematics in many ways‚ but one of the most important contributions he made was the creation of Binomial Coefficients; now known as Pascal’s Triangle. “Pascal’s triangle determines the coefficients which arise in binomial expansions”
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for the Binomial Distribution P(S) The symbol for the probability of success P(F) The symbol for the probability of failure p The numerical probability of a success q The numerical probability of a failure P(S) = p and P(F) = 1 - p = q n The number of trials X The number of successes The probability of a success in a binomial experiment can be computed with the following formula. Binomial Probability
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Biology 180 Problem Set 2 1. A population of marine gastropods has shell lengths that are normally distributed with a mean μ = 8 mm and variance σ2 = 2.15 mm2. a. what proportion of the population will have shell lengths between 6.5 mm and 8.5 mm? (3 points) b. what is the probability of finding a gastropod that has a shell length of exactly 7.5 mm? (1 point) c. if there are 1‚000 gastropods in an area‚ how many will have shell lengths greater than 5 mm? (3 points) 2. Childhood lead poisoning
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Math 116 - Chapter 6 review Name___________________________________ Provide an appropriate response. 1) Two random variables are normally distributed with the same mean. One has a standard deviation of 10 while the other has a standard deviation of 15. How will the graphs of the two variables differ and how will they be alike? 2) Which is larger‚ the area under the standard normal curve between -1 and 1‚ or the area under the standard normal curve between 0 and 2? Explain your reasoning
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Monday 9/23 on Chapters 5‚ 8‚ 9 (in lab) • Reading: chapters 13‚ 14‚15; SG 12‚ 17‚ 18‚ 19 • Probability‚ conditional probability‚ Bayes’ rule‚ binomial distribution Week 6 (10/1‚ 10/3) • Reading: chapter 15; SG 20‚ Notes on chance variables by Prof. Roger Purves • Continue probability‚ some discrete distributions (geometric‚ negative binomial‚ hypergeometric). Week 7 (10/8‚ ‚10/10) • MIDTERM 1 on Tuesday 10/8 on Chapters 1-5‚ 8-15‚ and associated content from SG • Reading (for Thursday):
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Exam 3 Study Guide Math 219 1. The probability that a randomly selected patient who visits the emergency room will die within 1 year of the visit is 0.05. (binomial probability distribution) a) What is the probability that exactly 1 of 10 randomly selected visitors to the ER will die within 1 year? b) What is the probability that fewer than 2 of 25 randomly selected visitors to the ER will die within 1 year? c) What is the probability that at least 2 of 25 randomly selected
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WEEK 10: TITLE: BINOMIAL THEOREM‚ COUNTING PRINCIPLE‚ PERMUTATION‚ AND COMBINATION Christina Bryant Define Binomial Coefficient. Give an example. Write the steps of a Graphing Utility to evaluate your Binomial Coefficient and the final answer. Binomial coefficients are a family of positive integers that occurs as coefficients in the binomial theorem. (10¦10) (10¦10)=10!/(10-10)!10! =10!/0!10! =10!/(1)(10!) =10!/10! =1 Final answer is 1. Explain the fundamental counting principle
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Introduction. The ’Stroop Effect ’ was first introduced in 1935. It originated from the theory of automatic processes. It is clear that some processing activities become automatic as a result of prolonged practice eg. Typing‚ driving‚ etc. Automatic processes therefore are fast‚ require no attention and are unavoidable. Stroop believed that there was some evidence that word identification may be a form of an automatic process. In the experiment participants had to name the colours in which the
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