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.

Stats 401 Week 2 Relative frequency = How many times appeared in category ÷ Total items in category (like finding percent without multiplying by 100 at the end) For the median, if there is an even amount of number given then add the two middle terms then divide by 2. EX: 1 2 3 4 5 6. The two middle terms are 3 and 4 so 3 + 4 = 7. Then 7/2 = 3.5 (finding the average of those numbers). If there isn’t a mode (1 2 3 4 5 6) then write “NO MODE” not “The mode is zero” because that implies that there is the number 0 and that is what appears the most. Peak of curve is in the middle When the mean = median = mode the distribution is bell shaped or symmetric. Median > mean then it is left skewed Med