Determining independence of a joint continuous probability distribtuion
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I'm just confused on determining if a joint pdf has independence between it's two variables X and Y. The theorem given to me is f(x,y) = fx(x)*fy(y) as a way to test independence, it's easy enough to understand But another theorem was given to me as an alternative f(x,y) = g(x)*h(y) where g(x) and h(y) are non-negative function of only x or y, respectively. How do I determine g(x) and h(y)? Is it just a factored form of f(x,y)? And if that's the case, is independence just determined on whether or not I can factor f(x,y)? An easy example: f(x,y) = 2y......so g(x)=y, h(y)=2? Likewise, is g(x)=4y and h(y) =.5 viable (although probably unnecessary)?
probability statistics probability-distributions
