Let X be a continuous random variable with density function f(x) 3/2 x ² -1 ≤ x ≤ 1. Sketch this density function. Use the central limit theorem to sketch the approximate density function S = X ₁ + ... + X ₅₀ where X _i is independent variables with density f. Similarly, sketch the approximate density functions of S/50 and S/Sqrt 50 for each sketch, label at the least three points on the horizontal axis.