Do Question 1, 2 and 4

Q1. Let Y be a geometric (p) random variable. a. Obtain a recursive formula for computing the probability function values of Y. b. Determine the mode of Y. C. Determine E(Y) and E[Y(Y+1)]. Use your results to obtain Var(Y). Q2. Let X be a negative binomial (k, p) random variable a. Obtain a recursive formula for computing the probability function values of X. b. Determine the mode of Y. Q3. Exercise 5.7 Q4. A tetrahedral die is a four-sided pyramid and has sides numbered from 1 through 4. Suppose that a fair tetrahedral die is to be rolled until each of the possible outcomes has occurred at least once. Derive the expected number of dice rolls required. Q1. Let Y be a geometric (p) random variable. a. Obtain a recursive formula for computing the probability function values of Y. b. Determine the mode of Y. C. Determine E(Y) and E[Y(Y+1)]. Use your results to obtain Var(Y). Q2. Let X be a negative binomial (k, p) random variable a. Obtain a recursive formula for computing the probability function values of X. b. Determine the mode of Y. Q3. Exercise 5.7 Q4. A tetrahedral die is a four-sided pyramid and has sides numbered from 1 through 4. Suppose that a fair tetrahedral die is to be rolled until each of the possible outcomes has occurred at least once. Derive the expected number of dice rolls required