One of two doctors, dr. hibbert and dr. nick, is called upon to perform a series of
n surgeries. let h be the indicator r. v. for dr. hibbert performing the surgeries, and
suppose that e(h)=p. given that dr. hibbert is performing the surgeries, each surgery
is successful with probability a, independently. given that dr. nick is performing the
surgeries, each surgery is successful with probability b, independently. let x be the
number of successful surgeries.
(a) find the joint pmf of h and x.
(b) find the marginal pmf of x.
(c) find the conditional pmf of h given x=k.