In: Statistics and Probability
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 < 22
(e),(f)f (x) = ke-x for 0 < x
(g),(h)f (x) = k where k > 0 and 101 < x < 101 + k