a. The event {X2 # y} is equivalent to what event involvingX itself?b. If X has a
Chapter 4, Problem 71(choose chapter or problem)
a. The event {X2 \(\leq\) y} is equivalent to what event involvingX itself?
b. If X has a standard normal distribution, use part (a)to write the integral that equals P(X2 \(\leq\) 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 v = 1 df[see (4.10)]. [Hint: Use the following identity.]
\(\frac{d}{d y}\left\{\int_{a(y)}^{b(y)} f(x) d x\right\}=f[b(y)] \cdot b^{\prime}(y)-f[a(y)] \cdot a^{\prime}(y)\)
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