Suppose X and Y are independent random variables, where Y is exponentially distributed with mean 1, and X has density function
fX(x) = 2x*exp{-x^2}
(x >= 0):
Find the CDF for Z = X^2 + Y .
I don't know what is CDF stand for.
That's easy.
I can give you the density instead of the CDF, the cdf is easy too.
http://en.wikipedia.org/wiki/Cumulat...ution_function
Let , then the density of W is...
when w>0 and zero otherwise.
Hence as well as X.
Since they are independent the sum is a , which gives you the density.
The cumulative distribution function is .