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How do we verbally state: $\large f(y\mid x)\;?$

I'm familiar with $f(x)$ as "$f$ of $x$" and $f(x,y)$ as "$f$ of $x$ and $y$" (or $f$ of $x, y$), but what does the vertical line mean and how to state this verbally so that a screen reader would read it correctly?

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    is this in the context of stats/probability, or more general? – 2017-01-04
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    @πr8 Yes, exactly the former. – 2017-01-04
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    How do *you* say $f(y\vert x)$ in that context (stats/probability)? Is its use unambiguous? (I.e., are there other contexts where the screen reader might encounter $f(y\vert x)$ for which the context is not stats/probability? – 2017-01-04
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    Inputting only $f(y\vert x)$, WA interprets it as $f(\text{BitOr}[y, x]),$ and then the output is $f(\text{BitOr}[x, y])$ – 2017-01-04
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    @Chelonian In this context, usually read the line as "given". Often it's used in a likelihood, e.g. $X\sim N(\mu,\sigma^2)\implies f(x|\mu,\sigma^2)=\frac{1}{\sqrt{2\pi\sigma^2}}\exp\left(\frac{(x-\mu)^2}{2\sigma^2}\right)$, where I'd say "$f(x|\mu,\sigma^2)$ is the likelihood of $x$ given the parameters $\mu,\sigma^2$". – 2017-01-04
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    @amWhy if directed at me: i can only remember encountering it in this context, but i'm not certain this is the only meaningful context. – 2017-01-04
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    I suggest that you look into conditional probabilities of discrete distributions to acquire a more intuitive understanding of the concept before you attempt to understand how conditional probabilities of continuous distributions are defined because there are many similarities between probability mass and density functions. – 2017-01-04
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    I just posted my comment above because in one context, it might be read in a different way that how it's read in some other context. – 2017-01-04
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    You might want to look at this question: [Is there a definitive guide to speaking mathematics?](http://math.stackexchange.com/questions/35496/is-there-a-definitive-guide-to-speaking-mathematics). – 2017-01-04

2 Answers 2

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We read $f(y \ | \ x)$ as "f of y, given x." This is useful when we talk about conditional probability distributions.

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F of y given x? This is what I heard in probability