題組內容

4. (20 %) Let $X_1, X_2, \ldots, X_n$ be a random sample from a population with p.d.f. $$f(x) = cx(1 - x), \quad 0 < x < 1$$

(c) Let \( \bar{X}_n = (X_1 + X_2 + \dots + X_n) / n \). Find the moment generating function of \( \bar{X}_n \).