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If X and Y are independent random variables with means E[X] = 2 and E[Y] = 3, what is the expected value of XY?Review LaterE[XY] = 5E[XY] = 6E[XY] = 7E[XY] = 8

Question

If X and Y are independent random variables with means E[X] = 2 and E[Y] = 3, what is the expected value of XY?Review LaterE[XY] = 5E[XY] = 6E[XY] = 7E[XY] = 8

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Solution

The expected value of the product of two independent random variables is the product of their expected values.

So, if X and Y are independent random variables with means E[X] = 2 and E[Y] = 3, then the expected value of XY, E[XY], is E[X]E[Y] = 23 = 6.

Therefore, E[XY] = 6.

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