12545 Rayleigh distribution Want solution in 3 hrs

A random variable y has a Rayleigh distribution, if and only if its probability distribution is given by:

f(y)=2(alpha)y^(-alpha y^2) , y>0 and alpha>0
f(y)=0 , elsewhere

a) Show that mean=(1/2)*squareroot(pie/alpha)

b) Show that the variance =(1/alpha)*(1-pie/4)