Discrete Probability Distributions

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What is a discrete probability distribution?

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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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CCSS.HSS.MD.A.4

CCSS.HSS.MD.A.3

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

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The expected value (E) is calculated by multiplying each possible outcome by its probability and summing all these products: E(X) = Σ [x * P(x)].

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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 of a random variable.

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What is the formula for calculating the mean from a frequency distribution?

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Mean = (Σ [x * f]) / N, where x is the value, f is the frequency, and N is the total number of observations.

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CCSS.6.SP.B.5C

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What does it mean for a distribution to be normally distributed?

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A normally distributed variable has a symmetric bell-shaped curve, characterized by its mean and standard deviation, where most observations cluster around the mean.

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What is the standard deviation in a probability distribution?

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The standard deviation measures the amount of variation or dispersion of a set of values in a probability distribution.

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How do you interpret the expected value in a real-world scenario?

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The expected value provides a long-term average outcome of a random process, helping to make informed decisions based on probabilities.

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CCSS.HSS.MD.B.5B

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

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The probabilities must sum to 1, ensuring that all possible outcomes are accounted for in the distribution.

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CCSS.HSS.MD.A.4

CCSS.HSS.MD.A.3

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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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What is the difference between a discrete and a continuous random variable?

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A discrete random variable can take on a countable number of values, while a continuous random variable can take on an infinite number of values within a given range.