Expected Value

Front

What is Expected Value?

Back

The 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 the Expected Value, multiply each possible outcome by its probability and then sum all these products. Formula: EV = Σ (X * P(X)) where X is the outcome and P(X) is the probability.

Front

What is the Expected Value of a random variable with outcomes 50, 20, and 5 with probabilities 0.1, 0.3, and 0.6 respectively?

Back

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

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In a community, 30% of households have 1 child, 43% have 2 children, and 27% have 3 children. What is the expected number of children?

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

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What is the Expected Value of a stock with a 40% chance of being worth $50, a 35% chance of $60, and a 25% chance of $70?

Back

EV = (50 * 0.4) + (60 * 0.35) + (70 * 0.25) = 20 + 21 + 17.5 = 58.5.

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What is the mean (expected value) of a probability distribution?

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The mean (expected value) is the average of all possible values of a random variable, weighted by their probabilities.

Front

What is the formula for calculating the mean of a discrete probability distribution?

Back

Mean = Σ (X * P(X)), where X is each outcome and P(X) is the probability of that outcome.

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What is the probability of getting exactly 6 heads in 10 tosses of a fair coin?

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Using the binomial probability formula: P(X=k) = (n choose k) * p^k * (1-p)^(n-k). For 6 heads: P(6) = (10 choose 6) * (0.5)^6 * (0.5)^4 = 0.205.

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What does 'n choose k' mean in probability?

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'n choose k' (denoted as C(n, k) or nCk) is the number of ways to choose k successes in n trials, calculated as n! / (k!(n-k)!).

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What is a probability distribution?

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A probability distribution is a function that describes the likelihood of obtaining the possible values that a random variable can take.