17. In Chapter 3, we de ned a negative binomial rv as the number of failures that occur before the r th success in a sequence of independent and identical success/failure trials. The probability mass function

(pmf) of X is

a. Suppose that r  2. Show that is an unbiased estimator for p. [Hint: Write out E( ) and cancel x  r  1 inside the sum.]

b. A reporter wishing to interview ve 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.