Suppose a continuous random variable X has a probability density function given by f(x) = kx²(1 – x) for 0 s x s1 and 0 otherwise. (a) Find the value of k that makes f(x) a probability density function. (b) Find the c.d.f. F (b) = P (X s b). (Hint: Remember that the c.d.f. is defined over the entire real line.) (c) Find P(0.20 s X|X < 0.50).

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