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Chapter 1
Warming Up

Stochastic processes are studied with a small set of probabilistic tools used over and over: writing a count as a sum of indicators, and computing an expectation, a probability or a variance by first conditioning on a well-chosen random variable. This chapter collects them.

1.1 Expectations of Sums
1.2 Conditional Expectation
1.3 Computing Expectations by Conditioning
1.4 Computing Probabilities by Conditioning
1.5 Markov’s Inequality
1.6 Computing Variances by Conditioning

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