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Marginal PDF from Joint PDF 
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#1
Nov2612, 11:27 PM

P: 4

Hi all,
I'm looking at the joint pdf F(x,y) = (8+xy^3)/64) for 1<x<1 and 2<y<2 (A plot of it is here: https://www.wolframalpha.com/input/?...y+from+2+to+2 ...sorry about the ugly url) and trying to find the marginal PDFs for X and Y. I know I want to integrate the joint function with respect to Y and X in order to to get the marginal pdfs for X and Y, respectively. However, I'm running into trouble when I try to set the bounds for these integrals! As far as I can tell, X and Y don't seem to depend on each other in this sense; i.e. for marginal(X) i would have Integral([JointPDF]dy), from 2 to 2, which comes out to 1/2. (Similarly, integrating with respect to x from 1 to 1 yields 1/4). When I integrate these from their respective bounds (x from 1 to 1, y from 2 to 2) both come out to 1, as a proper pdf should. However the fact that both are independent of x and y values makes me think something might be wrong...does anyone have any suggestions as to what I might be doing wrong? Thanks so much! Jamie Edit: My apologies! Posted this to the wrong place! I can't figure out how to delete it though :x 


#2
Nov2712, 10:39 AM

Sci Advisor
P: 3,252




#3
Nov2712, 12:04 PM

P: 4

Maybe I'm mistaking, but as far as I can tell the indefinite integral comes out to:
(8y+(xy^4)/4)/64 + c. If you evaluate this from 2 to 2, the x terms cancel because the y is an even function, i.e. from 2 to 2 we get [(1/4)+16x][(1/4)+16x], so (1/4)+(1/4)+16x16x = 1/2. This is what made me think that perhaps my bounds are incorrectly calculated... Am I doing something wrong? 


#4
Nov2712, 04:02 PM

Sci Advisor
P: 3,252

Marginal PDF from Joint PDF
For example, consider the events [itex] A = \{x: x \in [0, 1]\},\ B = \{y: y \in [0,1]\} [/itex] 


#5
Nov2812, 08:30 PM

P: 3

Still, what would the bounds be? A marginal pdf should not be a constant



#6
Nov2812, 09:30 PM

Sci Advisor
P: 3,252




#7
Nov2812, 11:14 PM

P: 21

I think a marginal pdf would be constant if X and Y are uniformly distributed, but I'm not sure how to tell if they are in this case. Any input?



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