{ localUrl: '../page/probability_distribution_countable.html', arbitalUrl: 'https://arbital.com/p/probability_distribution_countable', rawJsonUrl: '../raw/3tb.json', likeableId: '2584', likeableType: 'page', myLikeValue: '0', likeCount: '1', dislikeCount: '0', likeScore: '1', individualLikes: [ 'EricRogstad' ], pageId: 'probability_distribution_countable', edit: '8', editSummary: '', prevEdit: '7', currentEdit: '8', wasPublished: 'true', type: 'wiki', title: 'Probability distribution (countable sample space)', clickbait: 'A function assigning a probability to each point in the sample space.', textLength: '645', alias: 'probability_distribution_countable', externalUrl: '', sortChildrenBy: 'likes', hasVote: 'false', voteType: '', votesAnonymous: 'false', editCreatorId: 'TsviBT', editCreatedAt: '2016-06-11 06:40:48', pageCreatorId: 'TsviBT', pageCreatedAt: '2016-05-25 21:35:11', seeDomainId: '0', editDomainId: 'AlexeiAndreev', submitToDomainId: '0', isAutosave: 'false', isSnapshot: 'false', isLiveEdit: 'true', isMinorEdit: 'false', indirectTeacher: 'false', todoCount: '1', isEditorComment: 'false', isApprovedComment: 'true', isResolved: 'false', snapshotText: '', anchorContext: '', anchorText: '', anchorOffset: '0', mergedInto: '', isDeleted: 'false', viewCount: '51', text: '[summary: A probability distribution on a countable [3t4] $\\Omega$ is a [3jy] $\\mathbb{P}: \\Omega \\to [0,1]$ such that $\\sum_{\\omega \\in \\Omega} \\mathbb{P}(\\omega) = 1$.]\n\nDefinition\n===\n\nA probability distribution on a countable [3t4] $\\Omega$ is a [3jy] $\\mathbb{P}: \\Omega \\to [0,1]$ such that $\\sum_{\\omega \\in \\Omega} \\mathbb{P}(\\omega) = 1$. \n\nIntuition\n=====\n\nWe express a belief that "$x\\in \\Omega$ happens with probability $r$" by setting $\\mathbb{P}(x) = r$. 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