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2.4.6 Sums of Random Variables

Now let us draw N samples from the pdf and define the following linear combination of the samples:

where the parameters are real constants and the are real-valued functions. Since the are r.v.'s, and G is a linear combination of functions of the r.v.'s, G is also a r.v. We now examine the properties of G, in particular its expectation value and variance. Referring to our earlier discussion of the mean and variance of a linear combination, expressed as Eq. (9) and Eq. (15), respectively, we find