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

3. Joint (Intersection) Probabilities Joint Probability 2

4. 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

5. 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

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

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

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

9. Outcome Count Histogram 8

10. Event Probability Histogram 9

11. 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

12. 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

13. Event Probability Histogram 12

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

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