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(Solved) The joint probability mass function of two discrete variables X and Y is given by

Question: The joint probability mass function of two discrete variables X and Y is given by

\[\begin{aligned} & f\left( x,y \right)=\left\{ \begin{aligned} & c\left( 3x+y \right)\,\,\,\,\,\,\,\,\,x=0,1,2,\,\,\,y=2,3 \\ & 0\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\text{otherwise} \\ \end{aligned} \right. \\

& \\ \end{aligned}\]
  1. Find c .
  2. Find the marginal probability functions
  3. Compute \(E\left( X \right),\operatorname{var}\left( X \right)\)
  4. Are X and Y independent.

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