Let X be a random variable with pdf 4 f(x) B³ √2²e¬³¹³, 0 < x < ∞, ß> 0. [(a)] Show that 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 8. •((d)] Find the log-Likelihood function of B and then derive its maximum likelihood estimator (MLE) [(e)] Find unbiased estimators for the parameters B and 82, respectively. [(0)] Compare the MLE for ẞ and the unbiased estimator for 82. Paragraph BIE