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Show that the following functions are probability density functions for some value of k and determine...

Show that the following functions are probability density functions for some value of k and determine k. Then, determine the mean ((a),(c),(e),(g)) and variance ((b),(d),(f),(h)) of X. Round your answers to three decimal places (e.g. 98.765).

(a),(b)f (x) = kx2 for 0 < x < 8
(c),(d)f (x) = k(1 + 2x) for 0 < x < 21
(e),(f)f (x) = ke-x for 0 < x
(g),(h)f (x) = k where k > 0 and 121 < x < 121 + k

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orchestra answered 2 years ago
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