Notation - f(x,a) vs f(x;a)

[Legendre]

Homework Statement

Quick question...

I have seen both being used : f(x,a) and f(x;a). What is the usual convention? Are both acceptable to denote functions of 2 variables (in this case f is a function of both x and a). Or are there vital differences between the two that I don't know about?

Thanks! :)

Homework Equations

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The Attempt at a Solution

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[Mark44]

I don't recall ever seeing this notation -- f(x; a) -- being used.

 

[statdad]

notation like $$f(x;a)$$ is used in mathematical statistics when you want to show that a distribution depends on a parameter (real or vector-valued). for example, if you are talking about a normal distribution with some mean and standard deviation, writing
$$\theta = (\mu, \sigma)$$ the density would be indicated $$f(x;\theta)$$

it indicates that the function depends on $$x$$ and involves a parameter $$\theta$$ (so, as we say in statistics, by varying $$\theta$$ we obtain not one but a family of normal distributions.