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 discrete (taking specific values) or continuous (taking any value within a range).

Tags

CCSS.HSS.MD.A.2

Front

Define discrete random variable.

Back

A discrete random variable is one that has a countable number of possible values, such as the number of children in a household.

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Define continuous random variable.

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A continuous random variable can take any value within a given range, such as the height of students.

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What is the mean of a random variable?

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The mean (expected value) of a random variable is the average of all possible values, weighted by their probabilities.

Tags

CCSS.HSS.MD.A.2

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

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The standard deviation is calculated as the square root of the variance, which measures the spread of the random variable's values around the mean.

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What is a probability distribution?

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

Tags

CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

What is the formula for the expected value of a discrete random variable?

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E(X) = Σ [x * P(x)], where x is a value of the random variable and P(x) is the probability of x.

Tags

CCSS.HSS.MD.A.2

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What is the variance of a random variable?

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Variance measures how far a set of numbers are spread out from their average value. It is the average of the squared differences from the mean.

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What is the relationship between mean and standard deviation?

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The mean provides a measure of central tendency, while the standard deviation indicates the dispersion of the data around the mean.

Tags

CCSS.6.SP.A.3

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What does it mean if a random variable is normally distributed?

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A normally distributed random variable has a symmetric bell-shaped distribution, characterized by its mean and standard deviation.

Tags

CCSS.HSS.ID.A.4