In Chapter 3, we defined a negative binomial rv as the num- ber 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) = x+r-1 + x 1 ) p (1 - p) x = 0, 1, 2, ... x

a. Suppose that r2. Show that p=(-1)/(X+r-1) is an unbiased estimator for p. [Hint: Write out E(p) and cancel x + 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 pro- portion who support the candidate.