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 (4.10)]
