A vat contains millions of marbles. $20\%$ of them have the number “$6$” carved on them, and the rest have the number “$17$” carved on them.
A man possesses $3$ eggs. A marble is drawn from the vat, and then he is given that number of cartons of a dozen eggs each. Find the expected value, variance, standard deviation and moment generating function of $Y$, the number of eggs he will own. This is all the information that is given to me.
I calculated the variance to be $2787.84$ which seems a little high to me. Here is how I got my answer: $V(x)= [(12(6)+3)^2(.2) + (12(17)+3)^2(.8)] - 180.6^2= 2787.84$. Am I on the right track?
My post was removed previously. Am I asking this in a better way?