Important Discrete Probability Distributions 5-1 Chapter Goals After completing this chapter‚ you should be able to: Interpret the mean and standard deviation for a discrete probability distribution Explain covariance and its application in finance Use the binomial probability distribution to find probabilities Describe when to apply the binomial distribution Use Poisson discrete probability distributions to find probabilities 5-2 Definitions Random Variables A random variable represents
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Discrete and Continuous Probability All probability distributions can be categorized as discrete probability distributions or as continuous probability distributions (stattrek.com). A random variable is represented by “x” and it is the result of the discrete or continuous probability. A discrete probability is a random variable that can either be a finite or infinite of countable numbers. For example‚ the number of people who are online at the same time taking a statistics class at CTU on
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Chapter 6 Continuous Probability Distributions Case Problem: Specialty Toys 1. Information provided by the forecaster At x = 30‚000‚ [pic] [pic] Normal distribution [pic] [pic] 2. @ 15‚000 [pic] P(stockout) = 1 - .1635 = .8365 @ 18‚000 [pic] P(stockout) = 1 - .3483 = .6517 @ 24‚000 [pic] P(stockout) = 1 - .7823 = .2177 @ 28‚000 [pic]
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A useful distribution for fitting discrete data: revival of the Conway–Maxwell–Poisson distribution Galit Shmueli‚ University of Maryland‚ College Park‚ USA Thomas P. Minka and Joseph B. Kadane‚ Carnegie Mellon University‚ Pittsburgh‚ USA Sharad Borle Rice University‚ Houston‚ USA and Peter Boatwright Carnegie Mellon University‚ Pittsburgh‚ USA [Received June 2003. Revised December 2003] Summary. A useful discrete distribution (the Conway–Maxwell–Poisson distribution) is revived
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Probability Distribution Memo To: Howard Gray‚ CEO; Jean Dubois‚ VP Mechanical Watch Division; Uma Gardner‚ VP Production; Amanda Hamilton‚ VP Marketing After identifying the business problem of falling sales and an increase in rejections by the Swiss Official Chronometer Control‚ conducting a study for research will prove to identify a solution. Researchers performed a study of a sample population of 500 people. The study reveals 60% of the watches purchased are certified and the average
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watch the same amount and 8% said they watch more. Find the probability out of a randomly selected group of five that exactly three will say they watch less T.V. this year than last. a. Not binomial. b. N/A c. n=5 p=0.70 q=0.30 r: (0‚ 3.5) 2. There are 20 m&m’s candies in a dish. 8 are brown‚ three red‚ five green and four yellow. Two candies are picked from the dish at random. What is the probability that both are red? a. Binomial b. P(Success) = 6/20 = 3/10 P(Failure) = 14/20 = 7/10
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Tutorial on Discrete Probability Distributions Tutorial on discrete probability distributions with examples and detailed solutions. ------------------------------------------------- Top of Form | Web | www.analyzemath.com | | Bottom of Form | | Let X be a random variable that takes the numerical values X1‚ X2‚ ...‚ Xn with probablities p(X1)‚ p(X2)‚ ...‚ p(Xn) respectively. A discrete probability distribution consists of the values of the random variable X and their corresponding
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North Star Concert North Star.xls Best Guess‚ Worst Case‚ Best Case; and Continuous Uncertainties 3 Engine Services‚ Inc. Quick Start Guide to Crystal Ball Analyzing Uncertainty‚ Probability Distributions‚ and Simulation Learning Module: Crystal Ball Litigate Demo Engine Services.xls Language of Probability Distributions and Monte Carlo Simulation 4 Taurus Telecommunications Corporation: A New Prepaid Phone Card Learning Module: Tornado Sensitivity Taurus Telecommunications.xls Sensitivity Analysis
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EXERCISES (Discrete Probability Distribution) EXERCISES (Discrete Probability Distribution) P X x n C x p 1 p x BINOMIAL DISTRIBUTION n x P X x n C x p 1 p x BINOMIAL DISTRIBUTION n x 1. 2. 3. The probability that a certain kind of component will survive a given shock test is ¾. Find the probability that exactly 2 of the next 4 components tested survive. The probability that a log-on to the network is successful is 0.87. Ten users
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BINOMIAL THEOREM OBJECTIVES Recognize patterns in binomial expansions. Evaluate a binomial coefficient. Expand a binomial raised to a power. Find a particular term in a binomial expansion Understand the principle of mathematical induction. Prove statements using mathematical induction. Definition: BINOMIAL THEOREM Patterns in Binomial Expansions A number of patterns‚ as follows‚ begin to appear when we write the binomial expansion of a b n‚ where n is a positive integer
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