Identify each of the following statements as True or False. Briefly explain each of your answers.

(a) For every symmetric random variable X, the median of X equals the average of the first and third quartiles of X.

(b) For every random variable X, the interquartile range of X is greater than the standard deviation of X.

(c) For every random variable X, the expected value of X lies between the first and third quartile of X.

(d) If the standard deviation of a random variable equals zero, then so does its interquartile range.

(e) If the median of a random variable equals its expected value, then the random variable is symmetric