Suppose a random variable X has a probability density function given by O elsewhere f(x) = kx (1 x) 0≤x≤1 0 elsewhere a. Find the value of k that makes this a probability density function b. Find P (0.4≤ x ≤ 1) c. Find P(x ≤ 0.4) d. Find P (0.8 ≤ x))

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A: The probability density function is given by,

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Q: probabilities: A. P(X > 22) = B. P(X < 7.3) = C. P(7 < X < 20) = D. P(10 < X < 25) =

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