Expected Value

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What is Expected Value?

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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.

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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: EV = Σ (Outcome × Probability).

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What does it mean for a game to be 'fair'?

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A game is considered 'fair' if the expected value of the game is zero, meaning that the average outcome is neither a gain nor a loss over time.

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In the context of a lottery, how do you determine the expected value of a ticket?

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To find the expected value of a lottery ticket, calculate the probability of winning multiplied by the prize amount, then subtract the cost of the ticket.

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What is the Expected Value of rolling a fair die with a payout of $3 for rolling a 2 or 4?

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EV = (1/6 * 3) + (4/6 * 0) = 0.5, which means the expected value is $0.50.

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If a probability distribution has outcomes of 50, 20, and 5 with probabilities 0.1, 0.3, and 0.6 respectively, what is the expected value?

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EV = (50 * 0.1) + (20 * 0.3) + (5 * 0.6) = 5 + 6 + 3 = 14.

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What is the expected number of cars in an American household if the average is 1.75?

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The expected number of cars for a randomly chosen American household is 1.75.

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What is the significance of the mean in probability distributions?

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The mean of a probability distribution is the expected value, representing the center of the distribution and the average outcome.

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How does the concept of risk relate to Expected Value?

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Risk in decision-making can be assessed by comparing the expected value of different choices, helping to identify options with higher potential returns versus losses.

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What is a fair game in terms of Expected Value?

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A fair game has an expected value of zero, meaning that the average winnings equal the average losses over time.