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Joint Probability Density Function

After watching this video (https://www.youtube.com/watch?v=B7Fh6Bsf-ig), I have the following question:

We have known that the probability of a particular number in a continuous PDF is zero since it maintains zero area.

However, why a slice in a joint PDF is meaningful since it maintains zero volume at all?

Many Thanks

To simplify, you can think it as the marginal probability of X, integrating the function in respect of y, which should be a slice of the function.

But since the probability in a joint PDF. is defined by the volume (dydx) of the function, the why a slice of the function is okay?

[quote]原帖由 [i]whytellmewhy[/i] 於 2017-2-12 06:18 PM 發表 [url=http://www.discuss.com.hk/redirect.php?goto=findpost&pid=456283137&ptid=26441831][img]http://www.discuss.com.hk/images/common/back.gif[/img][/url]
To simplify, you can think it as the marginal probability of X, integrating the function in respect of y, which should be a slice of the function.

But since the probability in a joint PDF. is defined by the volume (dydx) of the function, the why a slice of the function is okay?

[/quote]
Do you mean f(x) when talking about a slice of the function?
If you want to calculate ∫∫ f(x,y) dy dx = ∫ [∫ f(x,y) dy] dx, obviously the first step is to find: f(x) =  ∫ f(x,y) dy, before attempting to calcuate the final answer ∫ f(x) dx.