Uniform distribution - Independent Randmo variables?

[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

 

[viraltux]

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

 

[mathman]

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

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.

 

[camillio]

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

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.

 

[chiro]

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

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).

 

[karlihnos]

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