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 x 1 r 2 1 x b pr

(1 2 p)x x 5 0, 1, 2, .

a. Suppose that r 2.

Show that

(r 1)/(X  r 1)

is an unbiased estimator for p. [Hint: Write out E( ) and cancel x  r 1 inside the sum.]

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.