If the moment generating function of X is Mt 25et 15e2t 2

If the moment generating function of X is M(t) = 2/5e^t + 1/5e^2t + 2/5e^3t find the mean,variance, and the probability distribution function of X.

Solution

mean=2/5+2/5+6/5=2

for variance=E(x²)-(E(x))² =24/5 -   2=14/5

P(X=1) = 2/5

P(X=2) = 1/5
P(X=3) = 2/5

else every where zero