Let X have a Weibull distribution with parameters = 2 and . Show that Y = 2 X2 / 2 has a chi-squared distribution

Let X have a Weibull distribution with parameters α = 2 and β. Show that Y = 2 X2 / β2 has a chi-squared distribution with ν = 2. [The cdf of Y is P(Y ≤ y); express this probability in the form P(X ≤ g(y)), use the fact that X has a cdf of the form in Expression (4.12), and differentiate with respect to y to obtain the pdf of Y.]