Data Science in Theory and Practice. Maria Cristina Mariani

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      More generally, if is a matrix of random variables, then the is the matrix of expectations with elements , i.e.:

      For a random vector , the mean vector consists of the means of each variable:

where . For example let be measurements on the first variable. Then the sample mean for the first variable is defined as follows:

      The sample mean can be computed from the measurements on each of the variables. Therefore, in general for sample means, we have:

      Example 3.2 Consider the following data matrix introduced in Example 3.1:

      Each receipt yields a pair of measurements, total dollar sales, and number of movies sold. To find the sample mean , we calculate the average of each column as follows:

      Therefore,

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