Answer: In Chapter 3, we defined a negative binomial rv as
Chapter 6, Problem 6.17(choose chapter or problem)
In Chapter 3, we defined a negative binomial rv as the number of failures that occur before the rth success in a sequence of independent and identical success/failure trials. The probability mass function (pmf) of X is nb(x; r, p) { pr (1 p)x x 0, 1, 2, . . . 0 otherwise a. Suppose that r 2. Show thatp (r 1)/(X r 1)is an unbiased estimator for p. [Hint: Write out E(p) andcancel x r 1 inside the sum.]b. A reporter wishing to interview five individuals who supporta certain candidate begins asking people whether (S)or not (F) they support the candidate. If the sequence ofresponses is SFFSFFFSSS, estimate p the true proportionwho support the candidate.
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