Explanation:
Since X and Y are independent, E(XY) = E(X) × E(Y).
Step 1: Calculate E(X)
Step 2: Calculate E(Y)
Step 3: Calculate E(XY)
Therefore, the expected value of the product of X and Y is 21.0.
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The following probability matrix contains the joint probabilities for random variables X = {2, 7, or 12} and Y = {1, 3, or 5}:
| Y | |||
|---|---|---|---|
| 1 | 3 | 5 | |
| X | |||
| 2 | 5% | 15% | 5% |
| 7 | 10% | 30% | 10% |
| 12 | 5% | 15% | 5% |
We are informed that (X) and (Y) are independent. What is the expected value of the product of X and Y, E(XY)?
A
15.0
B
21.0
C
30.5
D
35.0
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