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Chapter 3: Expectation and Variance

44 Chapter 3: Expectation and VarianceIn the previous Chapter we looked at probability, with threemajor themes:1. Conditional probability:P(A|B).2. First-step analysis for calculating eventual probabilities in a Calculating probabilities for continuous and discrete random this Chapter , we look at the same themes Expectation of a random variable is thelong-term average of the observing many thousands of independent random values from therandom variable of interest. Take the average of these random values. Theexpectation is the value of this average as the sample size tends to will repeat the three themes of the previous Chapter , but in a different Calculating expectations for continuous and discrete random Conditional Expectation : the Expectation of a random variableX,condi-tionalon the value taken by another random variableY.

3. Calculating probabilities for continuous and discrete random variables. In this chapter, we look at the same themes for expectation and variance. The expectation of a random variable is the long-term average of the random variable. Imagine observing many thousands of independent random values from the random variable of interest.

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