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2. Let X be a continuous random variable with pdf given by f(x) = k 6x...

2. Let X be a continuous random variable with pdf given by f(x) = k 6x − x 2 − 8 2 ≤ x ≤ 4; 0 otherwise.

(a) Find k.

(b) Find P(2.4 < X < 3.1).

(c) Determine the cumulative distribution function.

(d) Find the expected value of X.

(e) Find the variance of X

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