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One of two doctors, Dr. Hibbert and Dr. Nick, is called upon to perform a series of n
Chapter 7, Problem 3(choose chapter or problem)
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.
Questions & Answers
QUESTION:
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.
ANSWER:Step 1 of 4
Given data:
Given that 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.
The probability of performing the surgeries and each surgery being successful by Dr Hibbert is a, and the probability of performing the surgeries and each surgery being successful by Dr Nick is b.
Let X be the number of successful surgeries.