Probability Integral Transformation Question
I have the following problem presented to me. How would you go about solving this?
Suppose that Y has a c.d.f. given by:
F(y) = 1 - 9/(y^2), for y>=3
a.) Find a transformation G(U) so that G(U) has a c.d.f. F when U has a uniform distribution on the interval (0,1).
b.) Given that a random sample of size 3 from a uniform distribution on the interval (0,1) yielded the values 0.0058, 0.2048, and 0.7692, use the transformation derived in part (a) to give values associated with a random variable with the same distribution as Y.
How would you go about solving this? Thanks for any help. I greatly appreciate it.
Re: Probability Integral Transformation Question
To start you off I would have a look at the following result:r
Inverse transform sampling - Wikipedia, the free encyclopedia
(Look at how the inverse cumulative function of any random variable is related to the U[0,1] distribution).