AQ 4. (25 points) (a) Show that if X is a continuous random variable, then minE|X (1| 2 EIX m| where m is the median of X. (Assume m is in the support of X ) (b) Show that if the pdf of a random variable X is symmetric about :1: = b, then b must be the median m of the distribution. (0) Can an odd function be a pdf or pmf for a random variable? (Explain or prove your answer.) (Hint: An odd function is a function that satises f(:1:) : f (3:) for all a: E R.)