# Discrete Uniform Random Variable 2

• Oct 14th 2009, 05:14 PM
sirellwood
Discrete Uniform Random Variable 2
I have the question:

Explain why a discrete uniform random variable, X, on [a,b] has the same variance as a discrete uniform random variable, W, on [1,b-a+1].

Use this information to establish that

...I don't even know where to start http://static.thestudentroom.co.uk/i...onal/frown.gif so any help would be great cheers
• Oct 14th 2009, 07:33 PM
mr fantastic
Quote:

Originally Posted by sirellwood
I have the question:

Explain why a discrete uniform random variable, X, on [a,b] has the same variance as a discrete uniform random variable, W, on [1,b-a+1].

Use this information to establish that

...I don't even know where to start http://static.thestudentroom.co.uk/i...onal/frown.gif so any help would be great cheers

[a, b] --> [1, b - a + 1] suggests a horizontal translation of -a + 1: W = X - a + 1. And you should know that the shape of a distribution is unaffected by horizontal translation ....
• Oct 15th 2009, 04:52 AM
sirellwood
ah ok, so you are saying that Var(X)=(b-a)*(b-a)/12. and Var(W)=(b-a)*(b-a)/12
for the first one a=a, b=b; for the second one a=1, b=b-a+1; so...

Var(X1)=Var(W)?
• Oct 16th 2009, 12:04 AM
matheagle
$V(aX+b)=a^2V(X)$

The b, is a shift and that only changes the mean (center) not the variance (spread).

2b or not 2b? oh well it's 2am.