The document describes finding a random variable with a given moment generating function. It provides an example where the moment generating function is (0.3et + 0.7)8. This random variable follows a binomial distribution with probability of success p=0.7, probability of failure q=0.3, and number of trials n=8. A formula is given to calculate the probability of getting x successes.

1. For each of the following, find a random variable that would have the given moment generating
function. Determine the possible values of the random variable and give either a formula or table
showing the probabilities for the random variable. (a) m(t) = (0. 3et + 0. 7)8
Solution
a) Binomial distribution with p =0.7 and q = 0.3 and n = 8
P(X = x ) = 8Cx (0.7)^x(0.3)^(8-x)