79.

a. The event {X2 y} is equivalent to what event involving X itself?

b. If X has a standard normal distribution, use part

(a) to write the integral that equals P(X2 y).

Then differentiate this with respect to y to obtain the pdf of X2 [the square of a N(0, 1) variable].

Finally, show that X2 has a chi-squared distribution with n  1 df [see Expression (4.10)]. (Hint:

Use the following identity.)