In Chapter 3, we defined a negative binomial rv as the number of failures that occur bef...

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

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 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.