Random variable question

1. Feb 6, 2010

If I have random variable, P ~ U(1,2), am I correct in thinking that xP ~ U(1,2) also ? (where x is some constant), or does the range change?

Thanks.

2. Feb 6, 2010

EnumaElish

Since P is U(1, 2), Prob(P < p) = p - 1. Note Prob(P < 1) = 1 - 1 = 0 and Prob(P < 2) = 2 - 1 = 1.

Assume x > 0, then Prob(xP < p) = Prob(P < p/x) = ...

Does this help?

Last edited: Feb 6, 2010
3. Feb 8, 2010

So Prob(P<p/x) = p/x -1 ?

when p=x Prob = 0, and 2p = x, Prob = 1

So xP still follows a Uniform Distribution ~ U(1, 2).

It looks as though I've assumed this though.

4. Feb 8, 2010

torquil

if U(1,2) is the uniform distribution on (1,2), then the random variable xP would be distributed according to U(x,2x).

Torquil