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- Why can we use the Dirac delta function [itex] \delta [/itex] to represent a conditional pdf?

Hi,

I have a quick question about something which I have read regarding the use of dirac delta functions to represent conditional pdfs. I have heard the word 'mask' thrown around, but I am not sure whether that is related or not.

The source I am reading from states:

[tex] p(x) = \lim_{\sigma \to 0} \mathcal{N}(\mathbf{x}; \mu , \sigma^2) = \delta(x - \mu) [/tex]

which makes sense from a graphical standpoint. As we reduce the variance of a normal distribution, it tends towards the shape of a dirac delta function.

Now it says: "

and it is here where I am confused. There is no further explanation of this result. So I know that when the argument of the delta function is 0, it evaluates to 1. However, I cannot understand what is going on here and how to interpret this expression.

Any help or guidance would be greatly appreciated.

Thanks

I have a quick question about something which I have read regarding the use of dirac delta functions to represent conditional pdfs. I have heard the word 'mask' thrown around, but I am not sure whether that is related or not.

The source I am reading from states:

[tex] p(x) = \lim_{\sigma \to 0} \mathcal{N}(\mathbf{x}; \mu , \sigma^2) = \delta(x - \mu) [/tex]

which makes sense from a graphical standpoint. As we reduce the variance of a normal distribution, it tends towards the shape of a dirac delta function.

Now it says: "

*the dirac delta is useful as a conditional pdf when we know that [itex] y = f(x) [/itex], giving:*

[tex] p(y | x) = \delta(y - f(x)) [/tex]"[tex] p(y | x) = \delta(y - f(x)) [/tex]"

and it is here where I am confused. There is no further explanation of this result. So I know that when the argument of the delta function is 0, it evaluates to 1. However, I cannot understand what is going on here and how to interpret this expression.

Any help or guidance would be greatly appreciated.

Thanks