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PROBABILITY REVIEW PART 5 PROBABILITY FOR TEXT ANALYTICS Thomas Tiahrt, MA, PhD CSC492 Advanced Text Analytics

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Joint (Intersection) Probabilities Joint Probability 2

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Joint Probabilities 3 BABA 12345678Total 11/64 1/8 21/64 1/8 31/64 1/8 41/64 1/8 51/64 1/8 61/64 1/8 71/64 1/8 81/64 1/8 Total1/8 1 Probabilities from Rolling Two Eight-sided Dice

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Joint Probabilities 4 BABA 12345678Total 11/64 1/8 21/64 1/8 31/64 1/8 41/64 1/8 51/64 1/8 61/64 1/8 71/64 1/8 81/64 1/8 Total1/8 1 Probabilities from Rolling Two Eight-sided Dice Marginal Probabilities

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Joint Probabilities 5 BABA 12345678 123456789 2345678910 3456789 11 456789101112 5678910111213 67891011121314 789101112131415 8910111213141516 Sum of Pips from Rolling Two Eight-sided Dice

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Joint Probabilities 6 BABA 12345678 123456789 2345678910 3456789 11 456789101112 5678910111213 67891011121314 789101112131415 8910111213141516 Sum of Pips from Rolling Two Eight-sided Dice

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7 EventsFace Value Sum 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

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Outcome Count Histogram 8

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Event Probability Histogram 9

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Probabilities of a Loaded Die 10 OutcomeProbability {1}1/8 {2}1/16 {3}1/8 {4}1/16 {5}1/8 {6}1/16 {7}3/8 {8}1/16

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Joint Probabilities of Loaded Dice 11 BABA 12345678Total 11/641/1281/641/1281/641/1283/641/1281/8 21/1281/2561/1281/2561/1281/2563/1281/2561/16 31/641/1281/641/1281/641/1283/641/1281/8 41/1281/2561/1281/2561/1281/2563/1281/2561/16 51/641/1281/641/1281/641/1283/641/1281/8 61/1281/2561/1281/2561/1281/2563/1281/2561/16 73/643/1281/643/1281/643/1289/643/1283/8 81/1281/2561/1281/2561/1281/643/1281/2561/16 Total1/81/161/81/161/81/163/81/161 Probabilities from Rolling Two Loaded Eight-sided Dice

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Event Probability Histogram 12

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References 13 Sources: Foundations of Statistical Natural Language Processing, by Christopher Manning and Hinrich Schtze The MIT Press Discrete Mathematics with Applications, by Susanna S. Epp Brooks/Cole, Cengage Learning

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The end has come. End of Probability Slides Part 5 14