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 < 21
(e),(f)f (x) =
ke-x for 0 < x
(g),(h)f (x) =
k where k > 0 and 121 < x < 121
+ k