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

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- Dec 3rd 2008, 01:53 PMonemoretime29Characteristic 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, 02:20 PMcl85
You might want to show us what you have done so far.

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

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