Front

What is Expected Value?

Back

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.

Tags

CCSS.HSS.MD.A.2

Front

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

Front

What does a negative Expected Value indicate?

Back

A negative Expected Value indicates a loss in the long run if the scenario is repeated multiple times.

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CCSS.HSS.MD.A.2

Front

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

Back

The Expected Value of a fair six-sided die roll is 3.5, calculated as (1+2+3+4+5+6)/6.

Tags

CCSS.HSS.MD.A.2

Front

In probability, what does the term 'outcome' refer to?

Back

An outcome is a possible result of a random experiment or event.

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What is the Expected Value of a game where you win $10 with a probability of 0.5 and lose $5 with a probability of 0.5?

Back

EV = (10 * 0.5) + (-5 * 0.5) = 5 - 2.5 = $2.5.

Tags

CCSS.HSS.MD.B.5A

Front

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

How do you interpret an Expected Value of 0?

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An Expected Value of 0 indicates that, on average, there is no gain or loss in the long run.

Tags

CCSS.HSS.MD.A.2

Front

What is the Expected Value of a random variable with outcomes 1, 2, and 3, with probabilities 0.2, 0.5, and 0.3 respectively?

Back

EV = (1 * 0.2) + (2 * 0.5) + (3 * 0.3) = 0.2 + 1 + 0.9 = 2.1.

Tags

CCSS.HSS.MD.A.2

Front

What is the significance of the Expected Value in decision-making?

Back

The Expected Value helps in making informed decisions by providing a measure of the average outcome of different choices.

Tags

CCSS.HSS.MD.B.5B