Question: 33. A continuous random variable X has the probability density function f(x) = 3x2, 0 < x < 1 0, otherwise (a) Find the

33. A continuous random variable X has the probability density function f(x) =



3x2, 0 < x < 1 0, otherwise

(a) Find the c.d.f. F(x).

(b) Find the numerical values of F(1/3), F(9/10), and P(1/3 < X ≤ 1/2).

(c) Find the value of a which is such that P(X ≤

a) = 1/4 (a is the 25th percentile of X).

(d) Find the mean μ and variance σ2 of X.

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