November 2012
Intermediate to advanced
794 pages
22h 9m
English
book
Probability, Random Variables, and Random Processes: Theory and Signal Processing Applications
by John J. Shynk
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4.12 SAMPLE MEAN 
AND SAMPLE VARIANCE S2
One of the more important functions of several random variables is the sample mean which is also known as the arithmetic mean. (The geometric mean is (X1...XN)1/N.) Consider an experiment with repeated trials, such as consecutive coin tosses, where N outcomes are observed corresponding to N random variables 
. This type of repeated experiment can be viewed as a discrete-time random sequence which is covered in Chapter 6. For our purposes in this section, we only need to consider N random variables regardless of how they are generated, and which may or may not be mutually dependent. The sample mean is generally used to provide a measure of the average value of the resulting outcomes: it is an estimate of the mean.
Definition: Sample Mean The sample mean of random variables 
is
(4.228) 
which itself is a random variable.
In subsequent chapters, we discuss some interesting properties of 
. Here, we mention that although the sample mean is an unbiased ...
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