(a) Assume that E(X) = µ exists for a continuous random variable X. Show that if the probability density function for X satisfies f(a - x) = f(a + x) for all X then E(X) = a and the median of X is...

(a) Assume that E(X) = µ exists for a continuous random variable

X. Show that if the probability density function for X satisfies

f(a - x) = f(a + x) for all X then E(X) = a and the median of X

is also a.

(b) For the density function

for what value of a does the relation f(a - z) f(a + z) hold

for all real z?

( c) What are the expected value and theoretical median of the

standard normal distribution?