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# Expected Value

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.

# Expected Value - Properties

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

If $$E[4X ] = 16 ,$$ what is $$E[X] ?$$

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

If $$E[X] = 3 ,$$ what is $$E[3X + 1 ]?$$

If $$E[X] = 4, E[Y] = 4 ,$$ what is $$E[4X+3Y]?$$

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