Suppose that X ~ U(-2, 2). What is the DENSITY of Y = X^4? Note that if

Z ~ U(a, b) then it has density f(z) = 1/(b - a) and cdf F(z) = (z - a)/(b - a) for a < z < b.

So I used change of variables ie.

f(y^(1/4)) = 1/4*dx/dy = (1/4)*(1/4) * y^(-3/4)

and this is wrong. any ideas what is the mistake?