The probability p that a patient is cured by a drug is a ran

The probability p that a patient is cured by a drug is a random variable that varies from batch to batch of the drug. The probability density function of p is Suppose that 25 patients are given doses of the drug taken from the same batch. Let Y be the number of the 25 that are cured. Find E(Y). The number of defects in a yard of fabric, Y, has a Poisson distribution with parameter X. The parameter X is random with density Lot X1, X2, X3 be independent Bernoulli random variables with p = 2/3. Lot Y = X1X2X3. Find the moment generating function of Y. An actuary determines that the claim size for a certain class of accidents is a random variable, X, with moment generating function Calculate the standard deviation of the claim size for this class of accidents.

Solution