Statistics 6.1 Random Variables & Probability Distributions

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What is a Variable?

Back

A characteristic or attribute of a sample or population that changes or varies for different individuals or things.

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What is a Random Variable?

Back

A variable whose values depend on the outcomes of a random phenomenon.

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What is the expected value in probability?

Back

The long-term average value of a random variable, calculated as the sum of all possible values, each multiplied by its probability.

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How do you calculate the expected number of children in a household given probabilities?

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Multiply each number of children by its probability and sum the results. For example: (1 * 0.30) + (2 * 0.43) + (3 * 0.27) = 1.97.

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What is the expected value of Eva's coin flip if she wins $4 for heads and loses $3 for tails?

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Expected value = (0.5 * 4) + (0.5 * -3) = $0.50.

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What is a Discrete Variable?

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A variable that can take on a countable number of values, such as the number of cheeseburgers served each day.

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What is a Continuous Variable?

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A variable that can take on an infinite number of values within a given range, such as height or weight.

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What is a Probability Distribution?

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A function that describes the likelihood of obtaining the possible values that a random variable can take.

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What is the difference between a sample space and an event?

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A sample space is the set of all possible outcomes of a random experiment, while an event is a specific outcome or a set of outcomes from the sample space.

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What is the Law of Large Numbers?

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A principle that states as the number of trials increases, the experimental probability of an event will converge to its theoretical probability.