4. The joint probability distribution of X and Y is given in TABLE Q4 a. TABLE Q4 a | Y X | 1 | 2 | 3 | 4 | |---|---|---|---|---| | 1 | 0.04 | 0.14 | 0.23 | 0.07 | | 2 | 0.07 | 0.17 | 0.23 | 0.05 | Find i) the marginal distributions of X and Y. [2 marks] ii) the mean and variance of X. [4 marks] iii) the mean and variance of Y. [4 marks]
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Step 1
First, we need to find the marginal distributions of X and Y. To do this, we sum the probabilities along the rows for X and along the columns for Y. For X: P(X=1) = 0.04 + 0.14 = 0.18 P(X=2) = 0.23 + 0.07 = 0.30 P(X=3) = 0.07 + 0.17 = 0.24 P(X=4) = 0.23 + 0.05 = Show more…
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