Let X denote a random variable that follows a binomial distribution with parameters n=5, p=0.3, and Y denote a random variable that has a Poisson distribution with parameter = 6. Additionally, assume that X and Y are independent random variables.

(a) What are the possible values for (X, Y ) pairs.

(b) Derive the joint probability distribution function for X and Y. (with steps)

(c) Using the joint pdf function of X and Y, form the summation /integration (whichever is relevant) that gives the expected value for X4 + Y + 7.

(d) Using the joint pdf function of X and Y, set up the summation /integration (whichever is relevant) that gives the expected value for X, and COMPUTE its value.