b) Suppose the probability density function for the random variable

X is given by f(x ) = x for 0 < x< 4

=0 otherwise

I.Find the value of m such that P(x< m) = 0.5

II.Find the value of m such that P(x> m) = 0.25

C) Consider the following density function for the random variable X

F(x) =for 0 < x <c

=0 otherwise

I.Find the value of c for which f(x)is a properprobability density function. Draw a graph of this distribution

II.Find the mean and variance of X

III.Calculate the probabilitythat < X <