87. Recall that X is said to be a gamma random variable with parametersI mage if its density is

(a) If Z is a standard normal random variable, show that Image is a gamma random variable with parameters Image

(b) If Image are independent standard normal random variables, then Image is said to be a chi-squared random variable with n degrees of freedom. Explain how you can use results from Example 2.39 to show that the density function of Image is