1. Understanding Random Variables

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Probability Distributions

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Random variables help us understand and calculate the probabilities of different events. Learn how to use random variables in this lesson.


  1. Lesson Goal (00:24)

    The goal of this lesson is to learn about random variables.

  2. What is a Random Variable? (00:29)

    A random variable is a variable that can take on different values based on the outcome of one or more chance events.


    Examples of random variables can include the number of heads we get when we flip a coin a certain number of times, or the amount of rainfall in a particular city in a particular month. Random variables can be discrete or continuous. A discrete random variable can only take on a specific, countable set of values. For example, the number of heads in a series of coin flips can only be a whole number between zero and the number of coins flipped. By contrast, a continuous random variable can take on any value within a range. Therefore, rainfall amounts would be continuous.

  3. Creating a Probability Distribution (03:36)

    A probability distribution is a statistical function that describes all the possible values for a random variable and their associated probabilities. It can be represented using a table or a chart. The probability distribution of a random variable helps us identify which values are most likely and least likely.

  4. Mean and Standard Deviation of a Distribution (04:59)

    The mean and the variance or standard deviation are generally the two most important properties of a probability distribution. The mean represents the expected value of the random variable, and is usually denoted by the Greek letter mu. The variance and standard deviation measure how spread out the data is around the mean. A high variance indicates spread out data, a low variance indicates data clustered around the mean.

    The standard deviation is the square root of the variance, so if we know one we can always calculate the other. The standard deviation is denoted by the Greek letter sigma, and the variance is denoted by sigma squared.