題組內容

3. (30 %) Let random variables $X$ and $Y$ have the joint p.d.f. $$f(x, y) = cxy^3, \quad 0 < y < x < 1$$

(c) Calculate \( \operatorname{E}(X), \operatorname{E}(Y), \operatorname{Var}(X), \operatorname{Var}(Y) \) and \( \operatorname{Cov}(X) \).