- #1

Nikitin

- 735

- 27

## Homework Statement

Ok this might be a stupid question, but:

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-frc3/t31/q77/s720x720/10001118_10202561443653973_1625797585_o.jpg

Why is this the case? I think for all of this to be right, then the assumption of ##Y=u(X) \Leftrightarrow y=u(x)##. But how do I prove this?

## The Attempt at a Solution

An attempt: OK, assume ##X## has a probability distribution given by ##f(x)##, and ##Y=2X## has a probability distribution of ##g(x)##. Then if ##Y = u(X)##, with w being the inverse one-on-one function of u, ##P(X=x) = P(w(Y)=x) = P(Y=u(x))=P(Y=y=u(x))##.

This is as far as I got, but now I am confused. What to do?