Please answer D and E only Exercise 8Suppose that 70% of the people coming out of a particular exit of 116th Street Station are ColumbiaUniversity affiliates. You wait at the exit and ask 10 people whether they are Columbia affiliatesor not.(a*) What is the probability that the third, the fifth and the tenth person are Columbia affiliates?(b*) What is the probability that the third, the fifth and the tenth person are Columbia affiliatesand all others are not?(c*) What is the probability that you find exactly three Columbia affiliates?(d*) What is the expected number of Columbia affiliates in your sample? What is the variance ofthis number?(e*) Suppose you keep asking people until you find 10 that are not Columbia affiliates, and thenyou go home. How many people do you have to ask on average until you can go home?

Name: Please answer D and E only Exercise 8Suppose that 70% of the people co
Uploaded: 2024-03-20T06:46:03.000Z
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Description: Please answer D and E only Exercise 8Suppose that 70% of the people coming out of a particular exit of 116th Street Station are ColumbiaUniversity affiliates. You wait at the exit and ask 10 people whether they are Columbia affiliatesor not.(a*) What

Let us consider the event that a\the person coming out of the exit is a Columbian Affiliate is considered a success. The probability of success, p = 0.70 (given) Let X be the random variable denoting the number of successes. Then X will be a binomial variate with parameters n & p Part d: X ~ Binom(n, p) where n = 10 and p = 0.70 Then the expected value of X is E[X] = np = 10×0.70 = 7 Therefore, the expected number of Columbian affiliates in the sample is 7. And the variance of X is Var(X) = np(1-p) = 10×0.70×0.30 = 2.1 Part d: To get exactly 10 successes X will follow a negative binomial with parameter (x, r, p) Therefore, the number of trials at which the rth success occurs is P(n|r, p) =n-1r-1pr(1-p)n-r Hence the number of persons to be asked on an average for 10 Columbian affiliates is μ=rp=100.70 =14.28 ~14