Consider a random sample of x1, x2,...,xn observations from a Weibull distribution with parameters and and density function f(x) = x1ex ,

Consider a random sample of x1, x2,...,xn observations from a Weibull distribution with parameters

α and β and density function f(x) = 

αβxβ−1e−αxβ

, x> 0, 0, elsewhere, for α, β > 0.

(a) Write out the likelihood function.

(b) Write out the equations that, when solved, give the maximum likelihood estimators of α and β.