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(Solved): Please show work. Will upvote. Thank you! Problem 4 (15 points): The joint pmf of two random vari ...



Problem 4 (15 points): The joint pmf of two random variables, \( X \) and \( Y \), is given by
\[
p_{X, Y}(x . y)=\left\{\beg

Please show work. Will upvote. Thank you!

Problem 4 (15 points): The joint pmf of two random variables, \( X \) and \( Y \), is given by \[ p_{X, Y}(x . y)=\left\{\begin{array}{l} \frac{1}{3} \text { for }(x . y) \in\{(0,1),(1,0),(2,1)\} \\ 0 \text { otherwise } \end{array}\right. \] (a) Are \( X \) and \( Y \) independent? (b) Are \( X \) and \( Y \) uncorrelated?


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Here the random variable X can take values 0, 1, and 2 and
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