A function is a probability density function when its integral is 1. So just get whether the integrals are 1. Just be careful on (b) the integral has limits 0 to +oo.

(a) Solve the equation .2.

(a) Find the value of a that makes for a valid probability density function

(b) Evaluate the mean of this distribution

(c) Evaluate the variance of this distribution

(b) Once you find 'a' compute

(c) Find .

EDIT: Mistake, but too lazy to fix it.