Random Variables

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What is a random variable?

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A random variable is a numerical outcome of a random phenomenon. It can be classified as discrete or continuous.

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What is the difference between discrete and continuous random variables?

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Discrete random variables take on a countable number of distinct values, while continuous random variables can take on any value within a given range.

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Give an example of a discrete random variable.

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The number of students in a classroom is a discrete random variable.

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Give an example of a continuous random variable.

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The height of students in a school is a continuous random variable.

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What is a probability distribution?

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A probability distribution describes how the probabilities are distributed over the values of the random variable.

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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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What is the mean of a random variable?

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The mean (or expected value) of a random variable is the long-term average value of repetitions of the experiment it represents.

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CCSS.HSS.MD.A.2

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How do you calculate the mean of a discrete random variable?

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Multiply each possible value by its probability and sum all the results.

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What is standard deviation in the context of random variables?

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Standard deviation measures the amount of variation or dispersion of a set of values.

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How do you calculate the standard deviation of a discrete random variable?

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1. Find the mean. 2. Subtract the mean from each value and square the result. 3. Multiply by the probability of each value. 4. Sum these values and take the square root.