Characteristic Function of a Gamma Distribution

• Dec 3rd 2008, 02:53 PM
onemoretime29
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.
• Dec 3rd 2008, 03:20 PM
cl85
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 $i^2$