Use Theorem 5.9 to find the moment– generating function of Y = X – λ, where X is a random variable having the Poisson distribution with the parameter λ, and use it to verify that σ2Y = λ.
Answer to relevant QuestionsIf X1, X2, . . . , Xk have the multinomial distribution of Definition 5.8, show that the covariance of Xi and Xj is –nθiθj for i = 1, 2, . . . , k, j = 1, 2, . . . , k, and i ≠ j. Definition 5.8 The random variables ...A social scientist claims that only 50 percent of all high school seniors capable of doing college work actually go to college. Assuming that this claim is true, use Table I to find the probabilities that among 18 high ...A manufacturer claims that at most 5 percent of the time a given product will sustain fewer than 1,000 hours of operation before requiring service. Twenty products were selected at random from the production line and tested. ...An expert sharpshooter misses a target 5 percent of the time. Find the probability that she will miss the target for the second time on the fifteenth shot using (a) The formula for the negative binomial distribution; (b) ...Among the 300 employees of a company, 240 are union members, whereas the others are not. If 6 of the employees are chosen by lot to serve on a committee that administers the pension fund, find the probability that 4 of the 6 ...
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