6 The missing part is over the indicated interval Prove that f(x) = = , [0,4]...

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6 The missing part is over the indicated interval Prove that f(x) = = , [0,4] is a probability density function over the 4(x+1)2 and find each probability. (a). P(0 < x < 2). (b). P(2 < x <4) (c). P(1 < x < 3) (d). P(x ≤3) 7 find the expected value cted value, variance, and standard deviation for f(x) = ¾¼x(2 − x), [0,2]. 6 The missing part is over the indicated interval Prove that f(x) = = , [0,4] is a probability density function over the 4(x+1)2 and find each probability. (a). P(0 < x < 2). (b). P(2 < x <4) (c). P(1 < x < 3) (d). P(x ≤3) 7 find the expected value cted value, variance, and standard deviation for f(x) = ¾¼x(2 − x), [0,2].