The CPU time requirement X of a typical job can be modified by the following distribution

$\displaystyle P(X \le t) = \alpha (1-{e_1}^{-\lambda_1 t}) + (1-\alpha)(1-e^{-\lambda_2t}) $where $\displaystyle \alpha =0.6$, $\displaystyle \lambda_1 = 10 $ and $\displaystyle \lambda_2 = 1$.

Compute

i) probability density function of X

ii) the mean service time .

iii) Plot the distribution function and density function of X.