a. The event {X2 ≤y} is equivalent to what event involving X itself? b. If X has a sta...

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 X²has a chi-squared distribution with v = 1df [see (4.10)]. [Hint: Use the following identity.]