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

Question: 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

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.

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