Given f(x)=2x for 0<x<1

Also it says f(y)=?? for 0<y<x

Since they say F(x) is the marginal density, a instance of cdf (I'm very vague on this terminology); we can get the pdf by differentiating the marginal density f(x)=2x. Such that F(x)= (2x)' = 2 = F(x,y)

Ok, with magic I found some formulas:

F(x,y) = f(x|y)f(y) and

F(x,y) = f(y|x)f(x)

Determine the density of X, given Y=y means pdf of X given Y=y OR f(x|Y=y) = f(x|y) = F(x,y) / f(y) = 2/(2-2y) = 1/(1-y)

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ok, so my problem is how do you know the range of x is [y,1] and not [0,1]. Are you suppose to always ASSUME 0<x<1 and 0<y<x MUST COMBINE to be 0<y<x<1 AND you MUST change the ranges to 0<y<x and y<x<1 therefor changing the ranges of x to [y,1]. That's the only way it makes sense.

Ok, i think i'm just venting that I got fooled by the given range of x (marginal density range) which was clearly meant to trick you into using the wrong range for the pdf later. It's funny because when I started typing this up, I was clueless how the answer came about; then after typing it up and thinking about it more clearly... the answer just seems plain as paint.

I'm fairly new at this stuff, so feel free to correct any vocabulary I may have wrong.

Also it says f(y)=?? for 0<y<x

Since they say F(x) is the marginal density, a instance of cdf (I'm very vague on this terminology); we can get the pdf by differentiating the marginal density f(x)=2x. Such that F(x)= (2x)' = 2 = F(x,y)

Ok, with magic I found some formulas:

F(x,y) = f(x|y)f(y) and

F(x,y) = f(y|x)f(x)

**f(y) = integral of F(x,y) with respect to x; from the range of x from [?,?]**Determine the density of X, given Y=y means pdf of X given Y=y OR f(x|Y=y) = f(x|y) = F(x,y) / f(y) = 2/(2-2y) = 1/(1-y)

================================================

ok, so my problem is how do you know the range of x is [y,1] and not [0,1]. Are you suppose to always ASSUME 0<x<1 and 0<y<x MUST COMBINE to be 0<y<x<1 AND you MUST change the ranges to 0<y<x and y<x<1 therefor changing the ranges of x to [y,1]. That's the only way it makes sense.

Ok, i think i'm just venting that I got fooled by the given range of x (marginal density range) which was clearly meant to trick you into using the wrong range for the pdf later. It's funny because when I started typing this up, I was clueless how the answer came about; then after typing it up and thinking about it more clearly... the answer just seems plain as paint.

I'm fairly new at this stuff, so feel free to correct any vocabulary I may have wrong.

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