23. If X is a Weibull random variable with parameters (,), show that E[X] = 1/ (1 +1/) where ( y) is the gamma

23. If X is a Weibull random variable with parameters (α,β), show that E[X] = α

−1/β (1 +1/β)

where ( y) is the gamma function defined by

00 F(y)=x- dx Hint: Write E[X] = tat- exp(at } dt and make the change of variables x=at, dx=at-1 dt