Use repeated integration by parts to show that
This result is important because values of the distribution function of a Poisson random variable may thus be obtained by referring to a table of incomplete gamma functions.
Answer to relevant QuestionsDerive the formulas for the mean and the variance of the Poisson distribution by first evaluating E(X) and E[ X(X – 1)]. If 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 ...With reference to Exercise 5.45 and the computer printout of Figure 5.1, find the probability that among 10 cars stolen in the given city anywhere from 3 to 5 will be recovered, using (a) The values in the P(X = K) column; ...Use Chebyshev’s theorem and Theorem 5.3 to verify that the probability is at least 35 36 that (a) In 900 flips of a balanced coin the proportion of heads will be between 0.40 and 0.60; (b) In 10,000 flips of a balanced ...Among the 16 applicants for a job, 10 have college degrees. If 3 of the applicants are randomly chosen for interviews, what are the probabilities that (a) None has a college degree; (b) 1 has a college degree; (c) 2 have ...
Post your question