Let X be a continuous random variable with density function f (x) = 3x , -1 5 x _ 1. Sketch this density function. Use the central limit theorem to sketch 5.4 Problems 191 the approximate density function of S = X1 + . .. + X50, where the X; are independent random variables with density f. Similarly, sketch the approxi- mate density functions of S/50 and S/ V50. For each sketch, label at least three points on the horizontal axis