Understanding Uniformly Distributed Random Variables

[roadworx]

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.

 

[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?

 

[roadworx]

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?

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.

 

[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