Question: 12. (a) Let Z be a standard normal random variable. Show that the random variable Y = Z2 is gamma and find its parameters. (b)

12.

(a) Let Z be a standard normal random variable. Show that the random variable Y =

Z2 is gamma and find its parameters.

(b) Let X be a normal random variable with mean μ and standard deviation σ. Find the distribution function ofW =

X − μ

σ

2

.

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