Why is part C negative binomial? Can you explain why it can\'t be just binomial?
ID: 3149490 • Letter: W
Question
Why is part C negative binomial? Can you explain why it can't be just binomial? Find the moment generating function, Mx(), of Xx Find the moment generating function, Mx(t), of X (Hint: The expansion e-000 kk is valid for any real value y.) (c) How many advertisements do you expect a person to receive in the mail in one month? What is the variance of the number of advertisements received in the mail in one month? When a random dialing machine calls residential telephone numbers for an opinion poll, 20% of calls reach a live person. (a) Let X be the number of calls that reach a person when 15 calls are made in an opinion poll. i. What is the distribution of X? ii. What is the probability that two or fewer calls reach a person? ii. Find the mean and the standard deviation of X. (b) What is the expected number of calls until the first person is reached? (c) Let Y be the number of calls needed to reach five persons i. What is the distribution of Y? ii. What is the probability that exactly 11 calls are needed to reach five persons?Explanation / Answer
In the given situation the random variable of interest is reaching the call to a live person and probability of sucess( reaching the call to a live person) is 0.20.
In part C the number of successes is fixed i.e., 5 ( 5 persons ) negative binomial distribution is apt.to use rather than binomial distribution. Because the negative binomial distribution arises by the same process that gives rise to binomial distribution. In binomial distribution the number of successes (X) varies from 0 to n(total number of trials) when 'n' is fixed, where as, in the negative binomial distribution r(number of successes) is fixed and X( number of trials) is allowed to vary.
Since in part C number of successes(5) is fixed we use negative binomial distribution rather than binomial distribution.
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