Question

A restaurant serves three fixed-price dinners costing $12, $15, and $20. For a randomly selected couple dining at this restaurant, let X be the cost of the man's dinner and Y be the cost of the woman's dinner. The joint distribution of the discrete random variables X and Y is displayed in the table below: | | Y=12 | Y=15 | Y=20 | |---|------|------|------| | X=12 | 0.05 | 0.05 | 0.10 | | X=15 | 0.05 | 0.10 | 0.35 | | X=20 | 0 | 0.20 | 0.10 | i) Compute the marginal distributions of X and Y and their expected values. ii) Determine the distribution P(Z) of the total cost for dinner Z=X+Y. iii) Compute E(Z) from the distribution in ii) and compare it to the sum E(X)+E(Y). iv) Compute the covariance and correlation coefficient between X and Y.

          A restaurant serves three fixed-price dinners costing $12, $15, and $20. For a randomly selected couple dining at this restaurant, let X be the cost of the man's dinner and Y be the cost of the woman's dinner. The joint distribution of the discrete random variables X and Y is displayed in the table below:

|   | Y=12 | Y=15 | Y=20 |
|---|------|------|------|
| X=12 | 0.05 | 0.05 | 0.10 |
| X=15 | 0.05 | 0.10 | 0.35 |
| X=20 | 0    | 0.20 | 0.10 |

i) Compute the marginal distributions of X and Y and their expected values.
ii) Determine the distribution P(Z) of the total cost for dinner Z=X+Y.
iii) Compute E(Z) from the distribution in ii) and compare it to the sum E(X)+E(Y).
iv) Compute the covariance and correlation coefficient between X and Y.

Added by Megan P.

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