Exercises 8.9: 30, 37, 52

Also:

1. Let $Z$ be a standard normal random variable. Show that $Z^2$ has a gamma distribution. What are the parameters? Hint: We did this in a previous exercise.
2. Let $Z_1$ and $Z_2$ be independent identically distributed standard normal random variables. Show that $Z_1^2 + Z_2^2$ has an exponential distribution. Hint: Use the preceding problem along with Exercise 30 above.