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, which can take on different values based on the outcome of a random event.

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What are the two main types of random variables?

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The two main types of random variables are discrete random variables and continuous random variables.

Front

Define a discrete random variable.

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

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Define a continuous random variable.

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A continuous random variable is one that can take on an infinite number of values within a given range, often representing measurements.

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Give an example of a discrete random variable.

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An example of a discrete random variable is the number of heads when flipping a coin three times.

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Give an example of a continuous random variable.

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An example of a continuous random variable is the height of students in a classroom.

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What is the probability mass function (PMF)?

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The probability mass function (PMF) is a function that gives the probability that a discrete random variable is exactly equal to some value.

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What is the probability density function (PDF)?

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The probability density function (PDF) is a function that describes the likelihood of a continuous random variable taking on a particular value.

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How do you determine if a variable is discrete or continuous?

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A variable is discrete if it can take on a countable number of values, while it is continuous if it can take on any value within a range.

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What is an example of a situation that involves a discrete random variable?

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An example is counting the number of students who pass an exam.