Let X be a random variable with pdf f(x) 4 = 83 = x²e³½³,0 < x < ∞, ß> 0. [(a)] Show that fo f(x)dx = 1 ⚫[(b)] is the pdf f(x) member of the exponential family of distributions? Justify your answer. [(c)] Let X₁..., X, be a random sample that follow the same distribution as X. Find a sufficient statistic for the parameter ẞ. [(d)] Find the log-Likelihood function of ẞ and then derive its maximum likelihood estimator (MLE) • [(e)] Find unbiased estimators for the parameters ẞ and ẞ2, respectively. [(f)] Compare the MLE for ẞ and the unbiased estimator for 82.