Question: 5. Let $X_{1}, X_{2}, cdots, X_{n} $ denote a random sample from the following pdf $$ f(x mid theta)=left{begin{array}{cl} left(frac{1}{theta} ight) r x^{r-1} e^{-x^{r} /

$5. Let $X_{1}, X_{2}, \cdots, X_{n} $ denote a random sample$

5. Let $X_{1}, X_{2}, \cdots, X_{n} $ denote a random sample from the following pdf $$ f(x \mid \theta)=\left\{\begin{array}{cl} \left(\frac{1}{\theta} ight) r x^{r-1} e^{-x^{r} / \theta} & \text { if } x>0, \theta>0 0 & \text { otherwise } \end{array} ight. $$ where $r$ is a known positive constant. Find the MLE of $\theta$. SP.AS. 1200

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