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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 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, often representing measurements.

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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 determine if a set of probabilities is a valid probability distribution?

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Check if all probabilities are between 0 and 1 and if their sum equals 1.

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What is the probability of getting heads at least once when flipping a fair coin three times?

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7/8

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If P(X=5) = 0.11, what does this represent?

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This represents the probability of the random variable X taking the value of 5.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

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What is the expected value of a discrete random variable?

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The expected value is the long-term average or mean of all possible values of the random variable, weighted by their probabilities.

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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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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 variance in the context of random variables?

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Variance measures the spread of a set of values, indicating how much the values differ from the expected value.