First, and very much most importantly, you must specify a DOMAIN. I'm going to guess you mean , but [-5,5] is about the same on this one. Please think about complete definitions. Your life WILL be better.

With that, we can solve the silly "proportional" word. The probability, whatever it is, must sum to unity.

Solve for 'a'. I get a = 1.3153602668. You may have to employ some numerical methods.

Can you take it from there? Calculating the first two moments seems a good way to proceed.