Expected Value

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What is Expected Value?

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Expected Value (EV) is a calculated average of all possible outcomes of a random variable, weighted by their probabilities. It represents the long-term average if the experiment were repeated many times.

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CCSS.HSS.MD.A.2

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How do you calculate Expected Value?

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To calculate Expected Value, multiply each possible outcome by its probability and sum all these products. Formula: EV = Σ (outcome × probability).

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CCSS.HSS.MD.A.2

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What is the Expected Value of a random variable with outcomes 1, 2, and 3 with probabilities 0.3, 0.43, and 0.27 respectively?

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EV = (1 × 0.3) + (2 × 0.43) + (3 × 0.27) = 1.97.

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CCSS.HSS.MD.A.2

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If the Expected Value is negative, what does it indicate about the outcome?

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If the Expected Value is negative, it indicates that you are expected to lose in the long run.

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CCSS.HSS.MD.B.5B

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What is the relationship between Expected Value and decision-making?

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Expected Value helps in making informed decisions by evaluating the potential outcomes and their probabilities, guiding choices that maximize benefits.

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CCSS.HSS.MD.B.5B

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What does a higher Expected Value signify?

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A higher Expected Value signifies a more favorable outcome or a better return on investment in probabilistic scenarios.

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CCSS.HSS.MD.B.5B

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What is the Expected Value of a fair six-sided die?

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EV = (1+2+3+4+5+6)/6 = 3.5.

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CCSS.HSS.MD.A.2

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How does Expected Value apply to gambling?

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In gambling, Expected Value helps players understand the average outcome of bets over time, allowing them to assess the risk and potential reward.

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CCSS.HSS.MD.B.5B

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What is the Expected Value of two bags checked in at Southwest Airlines with a mean weight of 36 pounds?

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The Expected Value of the weights of two bags is 72 pounds (36 + 36).

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CCSS.HSS.MD.A.2

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What is the standard deviation of the weights of two bags if the standard deviation of one bag is 3.5 pounds?

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The standard deviation of the weights of two bags is calculated as: √(3.5² + 3.5²) = 4.95 pounds.