# Stochastic

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Unformatted text preview: ually denoted by ⌦, the capital Greek letter Omega. Example A.1. Flip three coins. The ﬂip of one coin has two possible outcomes, called “Heads” and “Tails,” and denoted by H and T . Flipping three coins leads to 23 = 8 outcomes: HHH HHT HT H T HH HT T T HT TTH TTT Example A.2. Roll two dice. The roll of one die has six possible outcomes: 1, 2, 3, 4, 5, 6. Rolling two dice leads to 62 = 36 outcomes {(m, n) : 1 m, n 6}. The goal of probability theory is to compute the probability of various events of interest. Intuitively, an event is a statement about the outcome of an experiment. Formally, an event is a subset of the sample space. An example for ﬂipping three coins is “two coins show Heads,” or A = {HHT, HT H, T HH } An example for rolling two dice is “the sum is 9,” or B = {(6, 3), (5, 4), (4, 5), (3, 6)} Events are just sets, so we can perform the usual operations of set theory on them. For example, if ⌦ = {1, 2, 3, 4, 5, 6}, A = {1, 2, 3}, and B = {2, 3, 4, 5}, then the union A [ B = {1, 2, 3, 4, 5}, the intersection A \ B = {2, 3}, and the complement of A, Ac = {4, 5, 6}. To introduce our next...
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## This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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