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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 its probability of occurrence.

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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 of a discrete random variable, multiply each possible value by its probability and sum all these products.

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CCSS.HSS.MD.A.2

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What is a probability distribution?

Back

A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What does it mean if the expected value is negative?

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If the expected value is negative, it indicates that, on average, you are expected to lose money in that scenario.

Tags

CCSS.HSS.MD.B.5B

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What is a fair game in terms of expected value?

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A fair game is one where the expected value is zero, meaning that neither the player nor the house has an advantage.

Tags

CCSS.HSS.MD.B.5B

Front

What is a continuous random variable?

Back

A continuous random variable is a variable that can take on any value within a given range or interval.

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What is the expected value of a fair die roll?

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The expected value of a fair die roll is 3.5, calculated as (1+2+3+4+5+6)/6.

Tags

CCSS.HSS.MD.A.2

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How do you interpret the expected value in a gambling scenario?

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In a gambling scenario, the expected value helps determine whether a bet is favorable or unfavorable based on the potential outcomes and their probabilities.

Tags

CCSS.HSS.MD.B.5B

Front

What is the formula for expected value in a lottery scenario?

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The expected value in a lottery scenario is calculated by summing the products of each prize's value and its probability, then subtracting the cost of the ticket.

Tags

CCSS.HSS.MD.A.2

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What is the significance of the law of large numbers in relation to expected value?

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The law of large numbers states that as the number of trials increases, the sample mean will converge to the expected value.

Tags

CCSS.HSS.MD.B.5B