A chi-squared variate with degrees of freedom equal to df has representation Z2 1

+· · ·+Z2 df , where Z1, . . . , Zdf are independent standard normal variates.

a. If Z has a standard normal distribution, what distribution does Z2 have?

b. Show that, if Y1 and Y2 are independent chi-squared variates with degrees of freedom df1 and df2, then Y1 + Y2 has a chi-squared distribution with df = df1 + df2.