The Poisson probability distribution‚ named after the French mathematician Siméon-Denis. Poisson is another important probability distribution of a discrete random variable that has a large number of applications. Suppose a washing machine in a Laundromat breaks down an average of three times a month. We may want to find the probability of exactly two breakdowns during the next month. This is an example of a Poisson probability distribution problem. Each breakdown is called an occurrence in Poisson
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Discrete Random Variables: Homework Exercise 1 Complete the PDF and answer the questions. |X |P(X = x) |X(P(X = x) | |0 |0.3 | | |1 |0.2 | | |2 | | | |3 |0.4 | | a. Find the probability that X = 2. b. Find the expected value. Exercise 2 Suppose that you are offered the following “deal.” You roll a die. If you
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SIDS31081 - Statistics Refresher 2006 – 2007 Exercises (Probability and Random Variables) Exercise 1 Suppose that we have a sample space with five equally likely experimental outcomes : E1‚E2‚E3‚E4‚E5. Let A = {E1‚E2} B = {E3‚E4} C = {E2‚E3‚E5} a. Find P(A)‚ P(B)‚ P(C). b. Find P(A U B) . Are A and B mutually exclusive? c. Find Ac‚ Bc‚ P(Ac)‚ P(Bc). d. Find A U Bc and P(A U Bc) e. Find P(B U C) Exercise 2 A committee with two members is to be selected from a collection of 30
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Probability Distribution Essay Example Suppose you flip a coin two times. This simple statistical experiment can have four possible outcomes: HH‚ HT‚ TH‚ and TT. Now‚ let the random variable X represent the number of Heads that result from this experiment. The random variable X can only take on the values 0‚ 1‚ or 2‚ so it is a discrete random variable Binomial Probability Function: it is a discrete distribution. The distribution is done when the results are not ranged along a wide range‚ but are
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THE MOMENTS OF A RANDOM VARIABLE Definition: Let X be a rv with the range space Rx and let c be any known constant. Then the kth moment of X about the constant c is defined as Mk (X) = E[ (X c)k ]. (12) In the field of statistics only 2 values of c are of interest: c = 0 and c = . Moments about c = 0 are called origin moments and are denoted by k‚ i.e.‚ k = E(Xk )‚ where c = 0 has been inserted into equation (12). Moments about the
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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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to the number of cars that pass through. Suppose the probabilities are 1/12‚ 1/12‚ 1/4‚ 1/4‚ 1/6‚ and 1/6‚ respectively‚ that the attendant receives $7‚ $9‚ $11‚ $13‚ $15‚ or $17 between 4:00 P. M. and 5:00 P. M. on any sunny Friday. Find the attendant’s expected earnings for this particular period. 4.7 By investing in a particular stock‚ a person can make a profit in one year of $4000 with probability 0.3 or take a loss of $1000 with probability 0.7. What is this person’s expected gain? 4.10 Two
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Random Variable and Its Probability distribution “A random variable is a variable hat assumes numerical values associated with the random outcome of an experiment‚ where one (and only one) numerical value is assigned to each sample point”. “A random variable is a numerical measure of the outcome from a probability experiment‚ so its value is determined by chance. Random variables are denoted using letters such as X‚Y‚Z”. X = number of heads when the experiment is flipping a coin 20 times. There
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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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