4. Let c be a positive real number. Define f(x)={1+cc2(1+x)ecx0x>0otherwise (a) Show that f(x)dx=1 (b) Suppose that X is a continuous random variable with f(x) as its probability density function. What is E[X] ? (c) What is Var(X) ? 5. Suppose that X is a random variable with probability density function f(x)=(x2+1)1 Let Y=1/X. Compute the probability density function for Y. Simplify your answer as much as possible..