Maximum likelihood estimator for the parameter

A Weibull random variable X has a pdf of the form

. . . . .\(\displaystyle f_X(x;\, \alpha,\, m)\, =\, \begin{cases} \dfrac{1}{a}\, m\, x^{m-1}\, e^{-x^m\, /\alpha} & , & 0\, <\, x\, <\, \infty\\ \\ 0 & , & \mbox{elsewhere} \end{cases}\)

...where and m are positive parameters. If m is known (and is a constant), find the maximum likelihood estimator for the parameter .

curlym said:

A Weibull random variable X has a pdf of the form

. . . . .\(\displaystyle f_X(x;\, \alpha,\, m)\, =\, \begin{cases} \dfrac{1}{a}\, m\, x^{m-1}\, e^{-x^m\, /\alpha} & , & 0\, <\, x\, <\, \infty\\ \\ 0 & , & \mbox{elsewhere} \end{cases}\)

...where

and m are positive parameters. If m is known (and is a constant), find the maximum likelihood estimator for the parameter

.

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