# 查看完整版本 : Joint Probability Density Function

whytellmewhy 2017-2-12 06:15 PM

## 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

whytellmewhy 2017-2-12 06:18 PM

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?

hkpal 2017-2-20 12:45 AM

[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.