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 an experiment is 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 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 + 0.9 = 2.1.

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What does a higher Expected Value indicate?

Back

A higher Expected Value indicates a more favorable outcome in terms of potential gains or benefits when making decisions.

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What is the Expected Value of a household with 30% having 1 child, 43% having 2 children, and 27% having 3 children?

Back

EV = (1 × 0.3) + (2 × 0.43) + (3 × 0.27) = 0.3 + 0.86 + 0.81 = 1.97.

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What is Return on Investment (ROI)?

Back

Return on Investment (ROI) is a measure used to evaluate the efficiency of an investment, calculated as (Net Profit / Cost of Investment) × 100.

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How do you determine which investment option has the greatest ROI?

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Compare the ROI percentages of each option. The option with the highest percentage is considered to have the greatest Return on Investment.

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?

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EV = (10 × 0.5) + (-5 × 0.5) = 5 - 2.5 = 2.5.

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

Back

Expected Value helps in making informed decisions by providing a statistical basis for evaluating potential outcomes and risks.

Front

What is a probability table and how is it used?

Back

A probability table lists outcomes and their associated probabilities, helping to visualize and calculate Expected Values more easily.