This document summarizes the solution to an exercise with three parts: 1) Part (a) finds the probability density function f(x) of a random variable X based on its integral from -infinity to infinity being 1. It determines that f(x) = 2 and a = 2. 2) Part (b) calculates the expected value E(x) of X by integrating x*f(x) from 0 to 1. It determines the expected value is 1/3. 3) Part (c) calculates the variance V(X) of X by finding its expected value E(X2) and subtracting the square of its expected value. It determines the variance is 1/