Chapter 4
Mathematical Expectation
4.1 Mean of a Random Variable
In Chapter 1, we discussed the sample mean, which is the arithmetic mean of the data. Now consider the following. If two coins are tossed 16 times and X is the number of heads that occur per toss, then the values of X are 0, 1, and 2. Suppose that the experiment yields no heads, one head, and two heads a total of 4, 7, and 5 times, respectively. The average number of heads per toss of the two coins is then
This is an average value of the data and yet it is not a possible outcome of {0, 1, 2}. Hence, an average is not necessarily a possible outcome for the experiment. For instance, ...
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