# Math Help - Characteristic Function of a Gamma Distribution

1. ## Characteristic Function of a Gamma Distribution

Suppose that X ~ G (n, l). Obtain the characteristic function of X, and use it to compute the mean and variance of X.

Thanks.

2. You might want to show us what you have done so far.

The characteristic function is just $\phi_X(t)=E[e^{itX}]$.

To compute the mean, just differentiate the characteristic function, set $t$ to zero and divide by $i$. Similarly, to get the variance, differentiate the characteristic function twice, set $t$ to zero and divide by $i^2$