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If you play roulette, are you going to break-even? Maybe sometimes, but not if you play forever, because the expected value is negative. The expected value finds the average outcome of random events.

If \(E[3X+Y] = 11\) and \(E[X] = 2,\) what is \( E[Y]?\)

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If \(E[4X ] = 16 ,\) what is \( E[X] ?\)

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If \(E[3X+9Y] = 6\) and \(E[3X+Y] = 5,\) what is \( E[X+Y]?\)

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If \( E[X] = 3 ,\) what is \(E[3X + 1 ]?\)

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If \(E[X] = 4, E[Y] = 4 ,\) what is \(E[4X+3Y]?\)

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