Statistics 6.1 Random Variables & Probability Distributions

Front

What is a discrete random variable?

Back

A discrete random variable is a variable that can take on a countable number of distinct values, often representing counts of items or occurrences.

Front

What is a continuous random variable?

Back

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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CCSS.6.SP.A.3

Front

What are the conditions for a probability distribution?

Back

A probability distribution must satisfy two conditions: all probabilities must be between 0 and 1 inclusive, and the sum of all probabilities must equal 1.

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CCSS.HSS.MD.A.3

CCSS.HSS.MD.A.4

Front

Define a random variable.

Back

A random variable is a variable whose values are determined by the outcomes of a random phenomenon.

Front

What is a variable in statistics?

Back

A variable is a characteristic or attribute that can take on different values for different individuals or items.

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CCSS.6.SP.B.5B

Front

What is the standard deviation in a probability distribution?

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The standard deviation is a measure of the amount of variation or dispersion in a set of values.

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How do you determine if a set of probabilities forms a valid probability distribution?

Back

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

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CCSS.7.SP.C.7B

Front

What is the difference between a sample and a population?

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A sample is a subset of a population, which is the entire group of individuals or items being studied.

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CCSS.7.SP.A.1

CCSS.HSS.IC.A.1

Front

What is the mean of a probability distribution?

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The mean is the expected value of a random variable, calculated as the sum of all possible values weighted by their probabilities.

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CCSS.HSS.MD.A.2

Front

What is a probability mass function (PMF)?

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A PMF is a function that gives the probability that a discrete random variable is equal to a specific value.