題組內容

3. (10%) Let X have the probability mass function $$f_X(x) = P[X = x] = \frac{3}{2} \left(\frac{1}{2}\right)^{2|x|}, x = \pm 1, \pm 2, \dots$$

(b) (5%) Find \( E[X] \) and \( Var(X) \). [A detailed derivation is required and the answer has to be simplified.]