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What is the expected value in probability?

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.

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CCSS.HSS.MD.A.2

Front

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

Back

Multiply each possible outcome 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

Front

What are the characteristics of a valid probability distribution?

Back

1. The sum of all probabilities must equal 1. 2. Each probability must be between 0 and 1.

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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?

Back

A negative expected value indicates that, on average, a player can expect to lose money in the long run.

Tags

CCSS.HSS.MD.B.5B

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What is the mean of a probability distribution?

Back

The mean is another term for the expected value, representing the average outcome.

Tags

CCSS.HSS.MD.A.2

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How do you find the mean of a probability distribution from a table?

Back

Multiply each outcome by its probability, then sum all the products.

Tags

CCSS.HSS.MD.A.2

Front

What is the standard deviation in probability?

Back

The standard deviation measures the amount of variation or dispersion in a set of values.

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How is standard deviation calculated for a probability distribution?

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1. Find the expected value (mean). 2. For each outcome, subtract the mean and square the result. 3. Multiply by the probability of each outcome. 4. Sum these values and take the square root.

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What is a fair game in probability?

Back

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

Tags

CCSS.HSS.MD.B.5B