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[See Solution] Random variables X and Y have the joint probability mass function given in the following table, where It is a positive constant. Find each of

Question: Random variables X and Y have the joint probability mass function given in the following table, where It is a positive constant. Find each of the following:

normalising constant $k$,
marginal probability functions, $p_{X}(x)$ and $p_{Y}(y)$,
conditional distribution of $X$ given that $Y=1$,
conditional expectation of $X$ given that $Y=1$,
covariance and hence the correlation between $X$ and $Y$. Are $X$ and $Y$ independent?

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[See Solution] Random variables X and Y have the joint probability mass function given in the following table, where It is a positive constant. Find each of

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