Suppose that random variables $X$ and $Y$, each with a finite number of possible values, have joint probabilities of the form $$P(X=x, Y=y) = f(x)g(y)$$ for some functions $f$ and $g$. How in the world would you find formulae for this? That doesn't even make sense.
Find formulae for $P(X=x)$ and $P(Y=y)$ in terms of $f$ and $g$
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probability
probability-theory
probability-distributions