(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

2. Relevant equations

If X and Y are statistically independent, then f(x,y) = g(x)h(y) where

[itex]g(x) = \int f(x,y) dy[/itex]

[itex]h(y) = \int f(x,y) dx[/itex]

3. The attempt at a solution

(a)

[itex]g(x) = \int f(x,y) dy = \int_{y=0}^{1-x} 6x\, dy[/itex]

[itex]\Rightarrow g(x)=6x(1-x)[/itex]

and

[itex]h(y) = \int f(x,y) dx = \int_{x=0}^{1} 6x \,dx[/itex]

[itex]\Rightarrow h(y)=3[/itex]

Thus h(y)g(x) [itex]\ne[/itex] f(x,y) and thus X and Y are NOT statistically independent.

Now before I move onto (b) look at the solution that the text gives.

I have no idea what is going on in the upper bound for the h(y) integral? They also went a different route with the solution, but I think that my way should work since it is a definition of independence. But clearly our h(y) functionsshouldbe the same. What am I missing?

Thanks,

Casey

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# Homework Help: Joint Probability FunctionStatistical Independence

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