121 views

### Sum of Discrete Random Variables [duplicate]

If I have two independent discrete random variables, say, $$X \in \{1,3,10,20\}$$ and $$Y \in \{2,3,5,9,11,15\}$$ and let $$Z = X + Y$$ be the sum of two variables. Also, each value taken by ...
11k views

### What is meant by a “random variable”?

What do they mean when they say "random variable"?
25k views

### Why do we need sigma-algebras to define probability spaces?

We have a random experiment with different outcomes forming the sample space $\Omega,$ on which we look with interest at certain patterns, called events $\mathscr{F}.$ Sigma-algebras (or sigma-fields) ...
34k views

### Why is the sum of two random variables a convolution?

For long time I did not understand why the "sum" of two random variables is their convolution, whereas a mixture density function sum of $f(x)$ and $g(x)$ is $p\,f(x)+(1-p)g(x)$; the arithmetic sum ...
17k views

### Empirical CDF vs CDF

I'm learning about the Empirical Cumulative Distribution Function. But I still don't understand Why is it called 'Empirical'? Is there any difference between Empirical CDF and CDF?