CvHS Probability Distributions and Expected Value

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What is a probability distribution?

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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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What is a discrete random variable?

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A discrete random variable is a type of variable that can take on a countable number of distinct values.

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What is a continuous random variable?

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A continuous random variable is a variable that can take on an infinite number of values within a given range.

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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 by its probability and sum all these products.

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CCSS.HSS.MD.A.2

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What is the mean of a probability distribution?

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

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What does it mean for a probability distribution to be valid?

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A valid probability distribution must satisfy two conditions: all probabilities must be between 0 and 1, and the sum of all probabilities must equal 1.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the probability of getting at least 4 correct answers on a 5-question true-false quiz?

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The probability of getting at least 4 correct answers is calculated using the binomial probability formula.

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CCSS.HSS.MD.A.2

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What is the formula for binomial probability?

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The binomial probability formula is P(X=k) = (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successes, and p is the probability of success.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the significance of rounding in probability calculations?

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Rounding is important in probability calculations to ensure that results are presented in a clear and concise manner, especially when dealing with averages.