One of two doctors Dr Hibbert and Dr Nick is called upon to

One of two doctors, Dr. Hibbert and Dr. Nick, is called upon to perform a series of nsurgeries. Let H be the indicator r.v. for Dr. Hibbert is performing the surgeries, and suppose that E(H)=p. Given that Dr. Hibbert is performing the surgeries, each surgery is a successful with probability a, independently. Given that Dr. Nick is performing surgeries, each surgery is successful with probability b, independently. Let X be the number of successful surgeries.

Find the joint PMF of H and X.

Find the marginal PMF of X.

Find the conditional PMF of H given X = k.

Solution