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

(a) f(x)= kx²for 0

(b) f(x)=k(1 +2x)for 0

(c) f(x) =k e^-xfor 0

(d) f(x)=kwhere k > 0 and 100 < x<(100 + k)

(1 b)

For each of the density functions in Problem 1 (a) , perform the following using Excel (Show the underlying computation in form of spreadsheet along with graphs)

(a) Graph the density function and mark the location of the mean on the graph.

(b) Find the cumulative distribution function.

(c) Graph the cumulative distribution function.