February 2019
Intermediate to advanced
634 pages
17h 41m
English
Content preview from Introduction to Probability, Second Edition, 2nd Edition
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4.9 *Using probability and expectation to prove existence
An amazing and beautiful fact is that we can use probability and expectation to prove the existence of objects with properties we care about. This technique is called the probabilistic method, and it is based on two simple but surprisingly powerful ideas. Suppose I want to show that there exists an object in a collection with a certain property. This desire seems at first to have nothing to do with probability; I could simply examine each object in the collection one by one until finding an object with the desired property.
The probabilistic method rejects such painstaking inspection in favor of random selection: our strategy is to pick an object at random from the collection and ...
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