A continuous probability density distribution for the random

variableXhas the form:

f(x) =ke^xif 0 <x <2 (the < should be equal to or less than)

=ke^(4-x)if 2 <x< 4

= 0 otherwise

Use integration to determine:

the value of k

(i) the mean of the distribution,

(ii) the variance of the distribution.

Your help would be very much appreciated