(a) state the (four) conditions necessary for a random variable x to have a binomial distribution. it is known that the probability of being dealt a full house in a hand of poker is .0014. in 1,000 hands of poker, let x be the number of times the dealer gives you a full house. (b) what is the exact probability distribution of x? ( justify your answer carefully.) (c) what are the expected value and variance of x? (simply state the results based on your answer in ( (d) use a poisson approximation to show that p(x > 2), the probability that you are dealt at least 2 full houses, is approximately equal to .408. (e) suppose that a random variable y function of y is m(t) = e^(e' –1). poisson(a). prove that the moment-generating