{"id":"W4362503337","doi":"10.1007/978-3-031-25326-3_4","title":"Weak Convergence of Sequences of Random Variables","year":2023,"lang":"en","type":"book-chapter","venue":"CMS/CAIMS books in mathematics","topic":"Probability and Risk Models","field":"Decision Sciences","cited_by":0,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Alberta","funders":"","keywords":"Mathematics; Central limit theorem; Independent and identically distributed random variables; Convergence of random variables; Random variable; Weak convergence; Equivalence (formal languages); Proofs of convergence of random variables; Convergence (economics); Sum of normally distributed random variables; Limit (mathematics); Illustration of the central limit theorem; Discrete mathematics; Pure mathematics; Applied mathematics; Mathematical analysis; Statistics; Computer science","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.003930588,0.001517732,0.001541796,0.003036801,0.0008808543,0.003820023,0.001605159,0.001516561,0.007661886],"category_scores_gemma":[0.01696753,0.0008673126,0.001687742,0.002232597,0.004323311,0.005472406,0.002681165,0.004998086,0.001774665],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001916753,"about_ca_system_score_gemma":0.001301886,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001278575,"about_ca_topic_score_gemma":0.0007527819,"domain_scores_codex":[0.998207,0.0006875492,0.0001032017,0.0002035798,0.0006976397,0.0001010112],"domain_scores_gemma":[0.9896582,0.007642716,0.0003737458,0.000626795,0.001305273,0.0003932754],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"not_applicable","study_design_scores_codex":[0.00001406445,0.000009858505,0.00008547165,0.00009177782,0.00001727809,0.0000326113,0.0000793367,0.003017019,0.0003254812,0.9825267,0.003012665,0.01078776],"study_design_scores_gemma":[0.000009387625,0.00001777926,0.0001587104,0.00004691539,0.0000079192,0.00008320946,0.00002410474,0.01626584,0.0001912984,0.973779,0.009407033,0.000008866842],"study_design_candidate":"not_applicable","study_design_consensus":null,"genre_codex":"methods","genre_gemma":"other","genre_scores_codex":[0.01782884,0.01455613,0.7796277,0.004153487,0.001250166,0.0000783954,0.0003232397,0.000237519,0.1819446],"genre_scores_gemma":[0.400745,0.03629531,0.2459252,0.003515422,0.004774242,0.001226483,0.001290762,0.0008472995,0.3053802],"genre_candidate":"other","genre_consensus":null,"teacher_disagreement_score":0.007661886,"threshold_uncertainty_score":0.02563155,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1672149275970563,"score_gpt":0.3519497342556167,"score_spread":0.1847348066585603,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}