If y has a binomial distribution with n trials and probability of success p, then the moment generating function for y is m(t) = (pet + q) n , where q = 1 − p. differentiate the moment generating function to find e(y ) and e(y 2 ). then find v (y ).

Step-by-step explanation:

It looks like every time the coefficient increases by 3 while the exponent increases by 1.

Notice it starts at zero so 3 is multiplied by (x+1) to make it start from 0

The exponent is simply n, because at the start is it zero , then 1, then 2, so on.

The upper limit is 45 because 45 - 0 = 45 terms