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Joint distributions.

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I need some serious help on this problem attached.

I can do all but a) and b) which is where I need help!

So if someone could give me some help with this question a) and b) that would be great.

Here is what I have so far:

I know the marginals for X and Y

f_X(x)=1 if x∈[0,1], 0 otherwise

and

f_Y(y)=1 if y∈[0,1], 0 otherwise

but I don't know what to do now.

Please help!
(edited 7 years ago)
Original post by cliveb2016
...


a)

If X,YX,Y are independent, then:

fX,Y(x,y)=fX(x)fY(y)f_{X,Y}(x,y)= f_X(x)f_Y(y)

And b)

F(x,y)=0y0xfX,Y(u,v)  dudvF(x,y) = \int_0^y\int_0^x f_{X,Y}(u,v) \; \text{dudv}

in this case.

Edit: And why am I on TSR a this time!
(edited 7 years ago)

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