# Uniform distribution - Independent Randmo variables?

1. May 14, 2012

### karlihnos

Hi guys,

I have this doubt but i am not sure, if i have an uniform distibution can i conclude that the events or random variables are independent?

Thank you

2. May 14, 2012

### viraltux

Could you please explain a little bit more about your data? How many random variables? Which of those variables are uniform...

3. May 14, 2012

### mathman

No. For example choose a random variable X from a uniform distribution (0,1) and then let
Y = 1 - X. X and Y are certainly not independent, but both have unform distributions.

4. May 15, 2012

### camillio

Generally, distribution without any additional information (e.g. parameters in some dists.) doesn't say anything about dependence. Uniformity of random variable only means, that its realizations are equiprobable, that is $\mathbb{P}[X=x_1] = \mathbb{P}[X=x_2] = ...$ where $X \sim U(a,b)$ and $x_i \in [a,b]$. The notion of (in)dependence is much more tricky. Are you talking about multiple uniformly distributed random variables? A nice example of correlated uniformly distributed rvs gave mathman.

5. May 15, 2012

### chiro

The test that will definitely tell if two variables are dependent is if E[XY] <> E[X]E[Y] for two variables X and Y.

The converse is not true though funnily enough: you can show that E[XY] = E[X]E[Y] but still have instances where you have dependent variables, although the case that this happens provides a kind of 'evidence' that they are independent (doesn't mean its conclusive though).

6. May 19, 2012

### karlihnos

Thanks to all. So i think the best way to look for it is the test that mentioned chiro.