a The event X2 curren 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 curren 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 Icirc frac12 1 df see (4 10) Use the following identity dy aly)

Question: a. The event {X2 ¤ y} is equivalent to what event involving X itself? b. If X has a standard normal distribution, use part (a)

a. The event {X2 ‰¤ y} is equivalent to what event involving X itself?
b. If X has a standard normal 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 with Î½ = 1 df [see (4.10)]. [Use the following identity.]

dy aly)

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