The discussion revolves around the interpretation of a notation used for probability distributions, specifically in the context of binomial distributions. Participants explore the meaning of the notation f(x) = (3 x) and its implications for probability calculations.
Participants generally agree that the notation relates to combinations and binomial distributions, but there is disagreement about its correct interpretation and whether it accurately represents a probability distribution. The discussion remains unresolved regarding the implications of the notation on the total probability.
There are limitations in the discussion regarding the assumptions made about the notation and the definitions of f(x). The potential need for a multiplier to ensure the distribution totals to 1 is also noted but not resolved.
Yes. It's the number of combinations of 3 things taken x at a time. It's usually read as "3 choose x."ProfuselyQuarky said:That's a combination, right? I haven't done those since last summer.
What is the definition of f(x)? The combination term is a coefficient of the probability term for exactly x.FactChecker said: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?
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.mathman said:What is the definition of f(x)? The combination term is a coefficient of the probability term for exactly x.
Good catch. That has to be it.HallsofIvy said: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.