Density of f_x (x) = 4x^4 for 0<x<1
Y=(x-1/4)^2 Z= X^-2
Determine density of Y
and Distribution of Z
The cdf of f_x (x) is invalid since F_x (x) = (4/5)x^5 so the limit to infinity does not equal 1 as a cdf should have. Am I missing something?
The Attempt at a Solution
density of Y P ((x-1/4)^2 =< x) = P(x =< sqrt(x) +1/4) = f (sqrt(x) +1/4) *(1/2)x^(-1/2) = (2/sqrt(2)) (sqrt(x) +1/4)^4 what are the bounds?
cdf of Z P(X^-2 =< x) = P(x <=-1/x) +P (X>= 1/x) = F(-1/x)+1-F(1/x) = 1-8/(5x^5) what are the bounds?