(a) Show that the maximum likelihood estimator $f(0, a$ of the beta random variable with $b=1$ is
$$
\hat{a}_{M I}=\left[\frac{1}{n} \sum_{j=1}^n \log X_j\right]^{-1} .
$$
(b) Generate a sample of 100 observations of the beta random variable with $b=1$ and $a=0.5$ to obtain the estimate for $a$. Repeat for $a=1, a=2$, and $a=3$.