Howtosignalprocessing
- Are functions of random variables independent?
- What is independent random variable?
- How do you define independence in terms of distribution functions for continuous random variables?
- Is random variable dependent or independent?
Are functions of random variables independent?
Independence of Random Variables
If X and Y are two random variables and the distribution of X is not influenced by the values taken by Y, and vice versa, the two random variables are said to be independent.
What is independent random variable?
Intuitively, two random variables X and Y are independent if knowing the value of one of them does not change the probabilities for the other one. In other words, if X and Y are independent, we can write P(Y=y|X=x)=P(Y=y), for all x,y.
How do you define independence in terms of distribution functions for continuous random variables?
In other words, X and Y are independent continuous random variables if and only if their joint density can be factored into a product of their (single variables) densities: fX,Y (x, y) = fX(x)fY (y) for all x, y.
Is random variable dependent or independent?
You can tell if two random variables are independent by looking at their individual probabilities. If those probabilities don't change when the events meet, then those variables are independent. Another way of saying this is that if the two variables are correlated, then they are not independent.
