ABSTRACT

In this chapter, the authors explain indicator random variables. Paying attention to the order of operations is crucial when working with expectation. The most important property of expectation is linearity: the expected value of a sum of r.v.s is the sum of the individual expected values. Using linearity, the expectation of the Negative Binomial follows without any additional calculations. Expectation is a single number summarizing the center of mass of a distribution. A single-number summary of the spread of a distribution is the variance. The Poisson distribution is often used in situations where the authors are counting the number of successes in a particular region or interval of time, and there are a large number of trials, each with a small probability of success. Like expected value, variance is a single-number summary of the distribution of a random variable. One important application of law of the unconscious statistician is for finding the variance of a random variable.