a. The event {y} is equivalent to what event involv- ing X itself?

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

(a) to write the integral that equals P(X2y). Then differenti- ate this with respect to y to obtain the pdf of X [the square of a N(0, 1) variable]. Finally, show that X has a chi-squared distribution with 1 df [see (4.10)]. [Hint: Use the following identity.] dy {(x) dx} = {b(v)] +b(v) - Fa(y)]-a'(y)