Let X and Y be independent standard normal random variables. Find the mgf of X2+Y2. What can you conclude about the distribution of X2+Y 2? (Hint: See Example 9.19.)

**Example 9.19**

Sum of i.i.d. exponentials is gamma. We have shown that the sum of i.i.d. exponential random variables has a gamma distribution. Here we prove the result using the mgfs. First find the mgf of the exponential distribution.