Suppose the random variable Y is the number of homes with a dust mite level greater than 2 micrograms per gram of dust in a sample of 4 homes.

1. Find the numerical value of E(Y)

2 .Find the numerical value of V(Y), the variance of Y

3. Make an R function called "mgfh" which will calculate the derivative of the MGF for the above discrete random variable Y. It must have only two arguments t and k. Where t is the constant in M_Y(t) and k instructs the function to make the kth derivative. The function prints the numerical value of the kth derivative to the command line.

mgfh(t=0, k = 1) gives what value?

\f