Discussion Problem_(17)

[duck]

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.

[Devika]

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.

[Devika]

integrate*

[Sinistral]

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

[Sumit]

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??????

[Devika]

Correction- thats 2y and 2x. My bad.

[duck]

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

[Sumit]

thanks Duck!!! you are doing a great job...n plz keep posting Discussions problems like that.....

[duck]

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