40. For each probability density function below, determine the mean and variance, if they exist, and define the median and mode.

(a) fðxÞ ¼ p 1 þ x2  1 Ið Þ 1;1 ðxÞ

(b) fðxÞ ¼ 4x3I½ 0;1 ðxÞ

(c) fðxÞ ¼ :3ð Þ :7 x1 If g 1;2;3;::: ðxÞ

(d) fðxÞ ¼ x 55 If g 1;2;:::;10 ðxÞ