2. Let f(x) be the PDF of some random variable X. f is said to be symmetric about a number a if for all > 0, f(a - ) = (a + ). (a) Show that if f(x) is symmetric around a number a, then the median of X is a. (b) Show that if f(x) is symmetric around a number a and E[X] exists, then E[X] : a. =