Expected Value

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What is the expected value in probability and statistics?

Back

The expected value is the long-term average or mean of a random variable, calculated as the sum of all possible values, each multiplied by their respective probabilities.

Tags

CCSS.HSS.MD.A.2

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How do you calculate the expected value of a discrete random variable?

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To calculate the expected value, multiply each possible outcome by its probability and then sum all these products.

Tags

CCSS.HSS.MD.A.2

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In the context of expected value, what does it mean if the expected value is greater than zero?

Back

If the expected value is greater than zero, it indicates a potential profit or gain in the long run.

Tags

CCSS.HSS.MD.B.5B

Front

What does it indicate if the expected value is less than zero?

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If the expected value is less than zero, it indicates a potential loss in the long run.

Tags

CCSS.HSS.MD.A.2

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What is the expected value of rolling a fair six-sided die?

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The expected value of rolling a fair six-sided die is 3.5.

Tags

CCSS.HSS.MD.A.2

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If you win $12 for rolling a six and $6 for rolling a one on a die, how do you find the expected value of this game?

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Calculate the expected value by multiplying the winnings by their probabilities: (1/6 * $12) + (1/6 * $6) + (4/6 * $0) = $3.

Tags

CCSS.HSS.MD.B.5A

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What is the expected value of a game where you pay $1 to roll a die and win $3 if you roll a 2 or a 4?

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The expected value is calculated as: (1/3 * $3) + (2/3 * $0) - $1 = $0.

Tags

CCSS.HSS.MD.B.5A

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What is the significance of the expected value in decision-making?

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The expected value helps in making informed decisions by providing a measure of the average outcome of uncertain events.

Tags

CCSS.HSS.MD.B.5B

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How does the concept of expected value apply to gambling?

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In gambling, the expected value helps players understand the average outcome of their bets over time, guiding their strategies.

Tags

CCSS.HSS.MD.B.5B

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What is a common misconception about expected value?

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A common misconception is that the expected value guarantees a specific outcome in a single trial; it only represents the average over many trials.

Tags

CCSS.HSS.MD.A.2