# Math Help - Variance from MGF

1. ## Variance from MGF

Could you please help me with the following, I know you have to differentiate but I am not saure if I am doing it right, could you please show intermediate steps.

If X has the moment generating function given by

MX(t) = cos(7.21t)+ 7.21t* sin(24.85t)

what is the variance of X ?

2. Originally Posted by javs156
Could you please help me with the following, I know you have to differentiate but I am not saure if I am doing it right, could you please show intermediate steps.

If X has the moment generating function given by

MX(t) = cos(7.21t)+ 7.21t* sin(24.85t)

what is the variance of X ?

You should know that:

$M_X'(0) = E(X)$.

$M_X''(0) = E(X^2)$.

Therefore $Var(X) = E(X^2) - [E(X)]^2 = M_X''(0) - [ M_X'(0) ]^2$.

If you show your working it will be much easier to check if you're "doing it right".