4.7 - Discrete Random Variables

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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, often representing counts or whole numbers.

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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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What are the properties of a valid probability distribution?

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1. All probabilities must be between 0 and 1. 2. 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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How do you calculate the expected value (mean) of a discrete random variable?

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The expected value is calculated by multiplying each possible value by its probability and then summing 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 to find the probability of at least k successes in a binomial distribution?

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It means calculating the probability of getting k or more successes in a fixed number of trials.

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What is the binomial probability formula?

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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 the mean in a probability distribution?

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The mean represents the average outcome you would expect if you repeated the experiment many times.

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How do you interpret a negative expected value in a gambling scenario?

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A negative expected value indicates that, on average, you would lose money if you played the game many times.

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CCSS.HSS.MD.A.2

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What is the difference between a fair game and an unfair game in terms of expected value?

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A fair game has an expected value of zero, while an unfair game has a negative expected value for the player.