Question: 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

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) =

a. Suppose that r ‰¥ 2. Show that
p^ = (t - 1) / (X + r - 1)
is an unbiased estimator for p.
b. A reporter wishing to interview five individuals who support a certain candidate begins asking people whether (S) or not (F) they support the candidate. If the sequence of responses is SFFSFFFSSS, estimate p = the true proportion who support the candidate.

p'(1-pr x=0, 1, 2,

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