Thread: help with computing density of one variable change.

Let X~exponential(lambda).Let Y=X^.75. Compute the density of fy of Y.

The answer to this is
fY(y) = 4(lambda)(y^3)e^(-lambda*y^4) for y > 0 and equals 0 for y <= 0.

My attempt:
Y=x^0.75
dx = 4dy / x^-0.75


i then get

integral from -inf to +inf of
4(lambda)(y^3)e^(-lambda*y^4) dy


from here i don't understand how to get to the answer

Originally Posted by Sneaky

Let X~exponential(lambda).Let Y=X^.75. Compute the density of fy of Y.

The answer to this is
fY(y) = 4(lambda)(y^3)e^(-lambda*y^4) for y > 0 and equals 0 for y <= 0.

My attempt:
Y=x^0.75
dx = 4dy / x^-0.75


i then get

integral from -inf to +inf of
4(lambda)(y^3)e^(-lambda*y^4) dy


from here i don't understand how to get to the answer

There are many ways of doing this. One simple way is to first get the cdf of Y:

for and zero otherwise.

Then the pdf is given by . Using the chain rule and the Fundamental Theorem of calculus is a simple way of doing this.