Uniform distribution - Independent Randmo variables?

In summary, the question is whether having a uniform distribution means that events or random variables are independent. The answer is no, as shown by examples and explanations from various contributors. The best way to determine dependence is by using a specific test, such as the one mentioned by chiro.
  • #1
karlihnos
2
0
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
 
Physics news on Phys.org
  • #2
Could you please explain a little bit more about your data? How many random variables? Which of those variables are uniform...
 
  • #3
karlihnos said:
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.
 
  • #4
karlihnos said:
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 [itex]\mathbb{P}[X=x_1] = \mathbb{P}[X=x_2] = ...[/itex] where [itex]X \sim U(a,b)[/itex] and [itex]x_i \in [a,b][/itex]. 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
karlihnos said:
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).
 
  • #6
Thanks to all. So i think the best way to look for it is the test that mentioned chiro.
 

1. What is a uniform distribution?

A uniform distribution is a probability distribution where all possible outcomes have an equal chance of occurring. This means that the values are spread out evenly across the range of possible values.

2. What are independent random variables?

Independent random variables are variables that have no influence on each other. This means that the value of one variable does not affect the value of the other variable.

3. How do you determine if variables are uniformly distributed?

To determine if variables are uniformly distributed, you can plot a histogram of the data and see if it forms a rectangular shape. You can also use statistical tests, such as the chi-square test, to check for uniformity.

4. What is the probability density function of a uniform distribution?

The probability density function of a uniform distribution is a constant value within the range of possible values, and 0 outside of that range. It can be represented by the formula f(x) = 1/(b-a), where a is the minimum value and b is the maximum value.

5. How is a uniform distribution useful in scientific research?

A uniform distribution is useful in scientific research as it allows for a fair and unbiased representation of all possible outcomes. It is commonly used in simulations and modeling, as well as for generating random numbers for experiments. It can also be used in statistical analysis to compare data sets and determine if they are evenly distributed.

Similar threads

I How to Express Non-regular Prior Distributions by Mathematical Formula
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
341
I Failure rate for a uniformly distributed variable
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
1K
Expectation of Product of three RVs
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
Rigorous mathematical definition of sampling
    • Set Theory, Logic, Probability, Statistics
Replies
13
Views
2K
A Uniform distribution setup
    • Set Theory, Logic, Probability, Statistics
Replies
8
Views
923
A Distribution of sum of two circular uniform RVs in the range [0, 2 pi)
    • Set Theory, Logic, Probability, Statistics
Replies
3
Views
646
I Parameters of a distribution of a physical variable
    • Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
MHB Burning time of Christmas Tree
    • Set Theory, Logic, Probability, Statistics
Replies
8
Views
684
I Probability paradox: P(X=x)=1/n >1
    • Set Theory, Logic, Probability, Statistics
Replies
5
Views
2K
B Sigma Multiplied Gaussian Distribution
    • Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K

Hot Threads

Recent Insights

Back
Top