Expected Value Practice

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.

Front

How do you calculate Expected Value?

Back

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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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.

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.

Front

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

Back

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

Front

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.

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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How do you interpret an Expected Value of 0?

Back

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

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.

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.