Let X be a continuous random variable with density function f (x) = 3/ 2 x2,−1 ≤ x ≤ 1. Sketch this density function. Use the central limit theorem to sketch the approximate density function of S = X1 + · · · + X50, where the Xi are independent random variables with density f . Similarly, sketch the approximate density functions of S/50 and S/ √ 50. For each sketch, label at least three points on the horizontal axis.
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