The mean and standard deviance (or variance) of a set of measurements are two common statistics to capture the centre and spread of the data. In this sequence of videos, we will see analogous measures of centre and spread for random variables and their corresponding probability distributions.
Expected Value of a Discrete Random Variable
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Notes on the video: Expected Value of a Discrete Random Variable
A point to consider for this video:
The expected value of a random variable is also commonly called the random variable’s expectation or the mean of the random variable. The next video discusses this use of the word “mean” versus the use of the word “mean” for the average of some data values.
Expected Value versus Sample Mean
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Notes on the video: Expected Value versus Sample Mean
A point to consider for this video:
Common notation for random variables and the corresponding values for sample data: The Greek letter μ is typically used for the mean (expected value) of a random variable, that is for a random variable X, E(X)=μ. The symbol x̅ is typically used for a sample mean calculated from data. For standard deviation, the Greek letter σ is used for the standard deviation (the square root of the variance) of a random variable while s is used for the sample standard deviation calculated from data.
Variance of a Discrete Random Variable
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Notes on the video: Variance of a Discrete Random Variable
Expected Value and Variance of a Discrete Random Variable: Two Example Problems
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Notes on the video: Expected Value and Variance of a Discrete Random Variable: Two Example Problems
The Expected Value and Variance of the Sample Mean
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Notes on the video: The Expected Value and Variance of the Sample Mean