7.61 The negative binomial variable X was defined as the number of the trial on which the r th success occurs in a sequence of independent trials with constant probability p of success on each trial. Let Xi denote a geometric random variable, defined as the number of the trial on which the first success occurs. Then we can write for independent random variables X1,…, Xr . Use results about mean and variance of a linear combination of random variables to show that

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