X is a random variable and it has has the uniform distribution with density 1/2 on [-1, 1]. Calculate the expectation E[X] and the variance Var(X). What is the distribution of Y = X3? Calculate its density. Solution Q2 a ) E(x) = integral (x/2dx) (-1,1) = 0 Variance = integral [(x-E(x))^2/2 dx] limits (-1,1) =1/3.