Verify that

(a) the Weibull density \(\alpha \beta x^{\beta-1} e^{-a x^{\beta}}, x>0\), corresponds to the distribution function \(F(x)=\) \(1-e^{-a x^{\beta}}, x>0\)

(b) the solution of \(u=F(x)\) is given by \(x=\) \(\left[-\frac{1}{\alpha} \ln (1-u)\right]^{1 / \beta}\).