Probability Distribution and Expected Value

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What is a probability distribution?

Back

A probability distribution is a mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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Define expected value in probability.

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

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CCSS.HSS.MD.A.2

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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 value of the random variable by its probability and sum all these products.

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CCSS.HSS.MD.A.2

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What is the formula for expected value (E(X))?

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

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CCSS.HSS.MD.A.2

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What does it mean if the expected value is greater than the mean of a dataset?

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It indicates that, on average, the outcomes are skewed towards higher values.

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What is the probability of an event?

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The probability of an event is a measure of the likelihood that the event will occur, ranging from 0 (impossible) to 1 (certain).

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CCSS.7.SP.C.5

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What is a random variable?

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A random variable is a variable whose possible values are numerical outcomes of a random phenomenon.

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Explain the difference between discrete and continuous random variables.

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Discrete random variables have countable outcomes, while continuous random variables can take any value within a given range.

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What is the significance of the sum of probabilities in a probability distribution?

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The sum of all probabilities in a probability distribution must equal 1, representing the certainty that one of the outcomes will occur.

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CCSS.7.SP.C.7A

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How do you find the probability of multiple events occurring?

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For independent events, multiply their individual probabilities. For dependent events, adjust the probabilities based on previous outcomes.

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CCSS.HSS.CP.A.2

CCSS.HSS.CP.A.4