# I What is meant by this notation?

1. Mar 10, 2016

### mohamed el teir

when saying the probability distribution of X is f(x) = (3 x) this is to be like vector notation where 3 is above x but i can't write it like this here. what is meant by this notation ?

2. Mar 10, 2016

### BvU

There is a vecor-like notation for the number of combinations ("n over k") but I don't know if that's what you are referring to:
$$\dbinom 3 x = {3!\over x!\, (3-x)!}$$(to me it seems a bit weird as a probability distribution...)

3. Mar 10, 2016

### mohamed el teir

that's right thank you !
i don't know why do they represent probability distributions by this notation

4. Mar 11, 2016

### Staff: Mentor

This notation is commonly used for binomial distributions.

$\dbinom 3 x$ is usually read as "3 choose x", the number of ways of choosing x items from a group of 3 of those items.

5. Mar 11, 2016

### Staff: Mentor

Yes. It's the number of combinations of 3 things taken x at a time. It's usually read as "3 choose x."

6. Mar 11, 2016

### FactChecker

One problem with that interpretation of the notation is that the distribution function will not total 1. Is it possible that the definition of f(x) is missing a multiplier?

7. Mar 11, 2016

### mathman

What is the definition of f(x)? The combination term is a coefficient of the probability term for exactly x.

8. Mar 11, 2016

### FactChecker

The original post stated: "the probability distribution of X is f(x) = (3 x) ". If we interpret that as f(x) = 3Cx, then it does not total 1.

9. Mar 12, 2016

### HallsofIvy

I suspect that the OP is completely misreading what is said and that it really is something that involves $\begin{pmatrix}3 \\ x \end{pmatrix}$ such as the binomial distribution with n= 3, $f(x)= \begin{pmatrix}3 \\ x \end{pmatrix} p^x (1- p)^{3- x}$ for x= 0, 1, 2, or 3.

10. Mar 12, 2016

### FactChecker

Good catch. That has to be it.