Question: I'm having trouble with this question. Please guide me through this. Let Z have the standard normal distribution. Then show that Y = Z 2

I'm having trouble with this question. Please guide me through this.

Let Z have the standard normal distribution. Then show that Y = Z2 will have the chi-squared distribution with 1 degree of freedom.

(You will have to start with the CDF of Y defined as FY (y) = P(Y y) = P(Z2 < y) = P( y Z y),

write final probability as an integral, and then use Liebnitz's Rule to differentiate the integral).)

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