CASE 2(Countably Infinite Sample Space): Whenis countablyinfinite, more care is required. Let 1,2,3,...where eachjis a distinct value. Associated with eachjis the probabilitypjPj,j1,2,....Of course, 0≤pj≤1 for allj.43
∙Because we can write j1j, and thejare disjoint sets,Pj1j∑j1pj1.∙With infinite, we cannot have equally likely outcomes (because thesum of the probabilities necessarily would be infinite).44
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