Each individual can be characterized as a success (S) or a failure (F), and there are M successes in the population. A sample of n individuals is selected without replacement in such a way that each subset of size n is equally likely to be chosen. The random variable of interest is X = the number of successes in the sample. MN - Mxn - xP(x) = Nn, for max(0, n – (N-M)) ≤ x ≤ min(n, M). E(X) = Mn Nand V(X) = N - nMMn 1 - N - 1NN853.68 A certain type of digital camera comes in either a 3-megapixel version or a 4-megapixel version. A camera store has received a shipment of 15 of these cameras, of which 6 have 3-megapixel resolution. Suppose that 5 of these cameras are randomly selected to be stored behind the counter; the other 10 are placed in a storeroom. Let X = the number of 3-megapixel cameras among the 5 selected for behind-the-counter storage. a. What kind of distribution does X have (name and values of all parameters)? b. Compute P(X = 2), P(X ≤ 2), and P(X ≥ 2). c. Calculate the mean value and standard deviation of X. 86The Negative Binomial Distribution The experiment consists of a sequence of independent trials. Each trial can result in either a success (S) or a failure (F). The probability of success is constant from trial to trial, so P(S on trial i) = p for i = 1, 2, 3, … The experiment continues (trials are performed) until a total of r successes have been observed, where r is a specified positive integer. X = the number of failures that precede the rthsuccess; the number of successes is fixed and the number of trials is random rxx + r - 1P(x) = p q, x = 0, 1, 2,...r - 1E(X) = r(1 - p)pand V(X) = 2r(1 - p)p873.75 Suppose that p = P(female birth) = .5. A couple wishes to have exactly two female children in their family. They will have children until this condition is fulfilled.