Discrete Probability Distributions and Expected Value

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What is a discrete probability distribution?

Back

A discrete probability distribution is a statistical distribution that describes the likelihood of each possible outcome of a discrete random variable, where the outcomes are countable.

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What is expected value in probability?

Back

Expected value is the long-term average or mean value of a random variable, calculated as the sum of all possible values, each multiplied by its probability of occurrence.

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How do you calculate the expected value of a discrete random variable?

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To calculate the expected value, multiply each possible outcome by its probability and sum all these products.

Front

What is the formula for expected value (E)?

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E(X) = Σ [x * P(x)], where x is a possible outcome and P(x) is the probability of that outcome.

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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 on average, players neither win nor lose money.

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If a die is rolled, what is the probability of rolling a 4?

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The probability of rolling a 4 on a fair six-sided die is 1/6.

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What is the probability of winning a raffle if you buy one ticket out of 500?

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The probability of winning is 1/500.

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In the context of a stock's expected value, what does a 40% chance of being worth $50 mean?

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It means that there is a 40% probability that the stock will be valued at $50 at the end of the year.

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How do you determine if you expect to win or lose in a raffle?

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Calculate the expected value of the prizes and compare it to the cost of the tickets.

Front

What is the expected value of Eva's coin flip if she wins $4 for heads and loses $3 for tails?

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The expected value is $0.50.