Let X be a continuous random variable with probability density function f (x) = 2x, 0 ≤...

Let X be a continuous random variable with probability density function f (x) = 2x, 0 ≤ x ≤ 1.

a. Find E(X).

b. Let Y = X2. Find the probability mass function of Y and use it to find E(Y ).

c. Use Theorem A in Section 4.1.1 to find E(X2) and compare to your answer in part (b).

d. Find Var(X) according to the definition of variance given in Section 4.2. Also find Var(X) by using Theorem B of Section 4.2.

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