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Discussion Problem_(17)

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Discussion Problem_(17)

duck
442 posts
1) Let (X,Y) be jointly  distributed  with pdf:
f(x,y) = 2 for 0<x<y<1 and
         = 0 otherwise.
Find marginal density function of x and y.

:)
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Re: Discussion Problem_(17)

Devika
90 posts
For marginal density of x, we'll intergrate the function wrt y , for 0<y<1.
So this comes out to be 2.
Similarly, the marginal density of y is 2.
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Re: Discussion Problem_(17)

Devika
15 posts
integrate*
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Re: Discussion Problem_(17)

Sinistral
288 posts
This post was updated on May 27, 2013; 10:48am.
In reply to this post by duck
f_1(x)= Integral (y=x to 1) f(x,y)dy
        =  Integral (y=x to 1) 2    dy
        = 2(1-x)          0<x<1

f_2(y)= Integral (x=0 to y) f(x,y)dx
        = Integral (x=0 to y)    2   dx
        = 2y           0<y<1
---
 "You don't have to believe in God, but you should believe in The Book." -Paul Erdős
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Re: Discussion Problem_(17)

Sumit
231 posts
In reply to this post by duck
Marginal density function of X:
fx(X)={2y for x<y<1} n zero otherwise

Marginal density function of Y:
Fy(Y)={2x for 0<x<y} n zero otherwise.

Plz confirm...

N also duck could u refer a book for probability distribution which is intuitive n sufficient for DSE n Also has solved examples...Actually the book (J.L Devore Probability & statistics) I'm referring just has concepts but not good questions...n also for other topics in Stats which book do you think is best??????
M.A Economics
Delhi School of Economics
2013-15
Email Id:sumit.sharmagi@gmail.com
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Re: Discussion Problem_(17)

Devika
15 posts
In reply to this post by Devika
Correction- thats 2y and 2x. My bad.
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Re: Discussion Problem_(17)

duck
442 posts
In reply to this post by Sinistral
Correct answer:
f(x)= 2(1-x) for  0<x<1
     = 0 otherwise

h(y)=2y for 0<y<1
      = 0 otherwise.


@Sumit:
http://economicsentrance.weebly.com/books.html
:)
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Re: Discussion Problem_(17)

Sumit
231 posts
thanks Duck!!! you are doing a great job...n plz keep posting Discussions problems like that.....
M.A Economics
Delhi School of Economics
2013-15
Email Id:sumit.sharmagi@gmail.com
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Re: Discussion Problem_(17)

duck
442 posts
Thanks Sumit.. :)
yup..will try to post as many as possible.. :)
:)