MATH 1228A/B
UWO
Course Overview
Grade Boosters
Lessons & Practice
1. Counting Methods
3hr1.3.1. Fundamental Counting Principle (FCP)*1.3.2. Example: Fundametal Counting Principle1.3.3. Practice: Fundamental Counting Principle1.3.4. Example: Fundamental Counting Principle w/ Cases1.3.5. Practice: Fundamental Counting Principle w/ Cases1.3.6. Example: Fundamental Counting Principle w/ Complements1.3.7. Subsets1.3.8. Example: Subsets1.3.9. Practice: Subsets1.3.10. Example: Subsets*
1.4.1. Factorial Symbol (!)1.4.2. Permutations (Extension of FCP)1.4.3. Example: Permutation1.4.4. Example: Permutations1.4.5. Practice: Permutations1.4.6. Example: Permutation w/ Repeated Objects1.4.7. Practice: Permutation w/ Repeated Objects1.4.8. Circular Permutation1.4.9. Example: Circular Permutation1.4.10. (Optional) Example: Non-Circular Permutation1.4.11. Practice: Circular Permutation1.4.12. Practice: Circular Permutation
1.5.1. Combinations1.5.2. Example: Combination Notation1.5.3. Practice: Combination Notation1.5.4. Deck of Cards Questions1.5.5. Example: Combinations1.5.6. Example: Combinations w/ Cards1.5.7. Practice: Combinations1.5.8. Practice: Combinations* (Must Try!)1.5.9. Practice: Combinations w/ Cards1.5.10. Example: Splitting up a Group w/ Combination
2. Probability
3hr2.1.1. Definitions: Experiment, Outcome, Sample Space2.1.2. Example: Equiprobably Sample Space (~2016 Test2 #1)2.1.3. Example: Sample Space (~2018 Test2 #3)2.1.4. Practice: Sample Space (~2017 Test2 #3)2.1.5. Properties of Probability2.1.6. Example: Properties of Probability (~2016 Test2 #3)2.1.7. Practice: Properties of Probability (~2018 Test2 #4)2.1.8. Practice: Properties of Probability (~2017 Test2 #2)2.1.9. Probability Table (very useful)2.1.10. Example: Probability Using Table (~2018 Test2 #5)2.1.11. Practice: Probability Using Table (~2017 Test2 #6)2.1.12. Example: Probability Using Table (~2018 Test2 #11)2.1.13. Practice: Probability Using Table (~2016 Test2 #4)
2.2.1. Calculating Probability2.2.2. Example: Equiprobable Sample Space (~2018 Test2 #7)2.2.3. Example: Line Permutation & Probability (~2018 Test2 #9)2.2.4. Example: Circle Permutation & Probability2.2.5. Practice: Circle Permutation & Probability2.2.6. Example: Dice & Probability (~2018 Test2 #8)2.2.7. Practice: Combination & Probability (~2017 Test2 #5)2.2.8. Example: Cards & Probability (~2016 Test2 #6)2.2.9. Practice: Cards & Probability (~2017 Test2 #7)2.2.10. Example: Distribution (Labelling) & Probability2.2.11. Example: Free Distributions & Probability (~2018 Test2 #21)
2.3.1. Conditional Probability and Independent Events2.3.2. Example: Conditional Probability & Table (~2018 Test2 #10)2.3.3. Practice: Conditional Probability (~2018 Test2 #12)2.3.4. Example: Dice & Conditional Probability2.3.5. Example: Cards & Conditional Probability (~2018 Test2 #18)2.3.6. Practice: Cards & Conditional Probability2.3.7. Practice: Cards & Conditional Probability2.3.8. Example: Circle Permutation & Conditional Probability2.3.9. Practice: Circle Permutation & Conditional Probability
2.4.1. Stochastic Process and Bayes’ Theorem2.4.2. Example: Stochastic Process (~2018 Test2 #13-15)2.4.3. Practice: Stochastic Process (~2017 Test2 #12)2.4.4. Example: Bayes' Theorem (~2018 Test2 #19)2.4.5. Practice: Bayes' Theorem (~2017 Test2 #19)2.4.6. Example: Bayes' Theorem (~2017 Test2 #21)2.4.7. Practice: Bayes' Theorem (~2016 Test2 #16)
2.5.1. Bernoulli Trials2.5.2. Example: Bernoulli Trials (~2018 Test2 #16)2.5.3. Example: Bernoulli Trials (~2017 Test2 #17)2.5.4. Practice: Bernoulli Trials (~2017 Test2 #16)2.5.5. Example: Bernoulli & Conditional Probability2.5.6. Practice: Bernoulli Trials & Conditional Probability (~2018 Test2 #18)2.5.7. Example: Solving for n* (~2016 Test2 #18)2.5.8. Practice: Solving for n* (~2017 Test2 #18)2.5.9. Independent Trials w/ More Than 2 Outcomes2.5.10. Example: Independent Trials (~2017 Test2 #20)2.5.11. Practice: Independent Trials (~2018 Test2 #17)
3. Working With Discrete Random Variables
1.9hr3.1.1. Random Variable & Probability Distribution Function3.1.2. Example: PDF (~2018 Final A18)3.1.3. Practice: PDF (~2017 Final A20)3.1.4. Example: PDF (~2017 Final B3c)3.1.5. Practice: PDF (~2017 Final B3c)3.1.6. Cumulative Distribution Function (CDF)3.1.7. Example: CDF (~2018 Final B4)3.1.8. Practice: CDF (~2017 Final A18, 19)3.1.9. Bionomial Random Variable3.1.10. Example: Binomial RV (~2017 Final A24)3.1.11. Practice: Binomial RV (~2016 Final B3)3.1.12. Example: Binomial RV (~2016 Final A26)3.1.13. Practice: Binomial RV (~2016 Final B4ab)
3.2.1. Expected Value or Mean 3.2.2. Example: Expected Value (~2018 Final A19)3.2.3. Practice: Expected Value (~2017 Final A21)3.2.4. Example: Expected Value (~2018 Final A20)3.2.5. Practice: Expected Value (~2016 Final A22)3.2.6. Variance and Standard Deviation 3.2.7. Example: Variance (~2018 Final A21)3.2.8. Example: Variance (~2018 Final A22)3.2.9. Practice: Variance (~2017 Final A22)
3.3.1. Formulas for Discrete RVs3.3.2. Example: Functions of Discrete RVs (~2018 Final A24)3.3.3. Practice: Functions of Discrete RVs (~2018 Final A23)3.3.4. Example: Functions of Discrete RVs3.3.5. Practice: Functions of Discrete RVs (~2016 Final A24)3.3.6. Independent Random Variables & Joint Distribution3.3.7. Example: Independent RVs (~2018 Final A26, 27)3.3.8. Practice: Independent RV (~2017 Final A25)3.3.9. Example: Joint PDF (~2017 Final A23)3.3.10. Practice: Independent RVs (~2018 Final A25)3.3.11. Example: Independent RVs (~2018 Final A27)3.3.12. Practice: Independent RV (~2017 Final A26, 27)
3.P.1. Additional Practice PDF3.P.2. Additional Practice PDF3.P.3. Additional Practice PDF3.P.4. Additional Practice PDF3.P.5. Additional Practice CDF3.P.6. Additional Practice PDF & CDF3.P.7. Additional Practice PDF & CDF3.P.8. Additional Practice PDF3.P.9. Additional Practice PDF & E(X)3.P.10. Additional Practice Binomial3.P.11. Additional Practice Binomial3.P.12. Additional Practice Binomial3.P.13. Additional Practice Expected Value3.P.14. Additional Practice Variance & Expected Value3.P.15. Additional Practice Variance
4. Using Continuous Random Variables
2hr4.1.1. Continuous RV & Probability Density Function4.1.2. Example: Probability Density Function (~2016 A27)4.1.3. Practice: Probability Density Function (~2016 Final A27)4.1.4. Example: Probability Density Function (~2017 Final A28)4.1.5. Practice: Probability Density Function (~2018 Final A28)4.1.6. Approximation & Continuity Correction4.1.7. Example: Approximating X Using Y (~2016 Final A28)4.1.8. Practice: Approximating X Using Y (~2018 Final A29)4.1.9. Example: Finding What is Approximated by Y (~2015 Final A27)4.1.10. Practice: Finding What is Approximated by Y (~2017 Final A29)
4.2.1. Normal RV & Standard Normal RV4.2.2. Example: Standard Normal RV (~2017 Final A31,32)4.2.3. Practice: Standard Normal RV (~2018 Final A30,31)4.2.4. Example: Standard Normal RV Given Probability (~2017 Final A33, ~2018 Final A32)4.2.5. Practice: Standard Normal RV Given Probability (~2016, 2017 Final A30)4.2.6. Finding the Probability of a Normal RV4.2.7. Example: Normal RV (~2018 Final A34, 35)4.2.8. Practice: Normal RV4.2.9. Practice: Normal RV (~2017 Final A34)4.2.10. Example: Normal RV Word Problem4.2.11. Example: Finding Mean (~2017 Final B4)4.2.12. Practice: Finding Standard Deviation (~2016 Final A34)4.2.13. Example: Finding the Value of a Normal RV(~2016 Final A33)4.2.14. Practice: Finding the Value of a Normal RV4.2.15. Bonus: Finding Mean and Standard Deviation*
4.3.1. Normal Approximation to the Binomial Distribution4.3.2. Example: Normal Approximation (~2017 Final A35)4.3.3. Practice: Normal Approximation (~2016 Final A35)4.3.4. Example: Normal Approximation of a Binomial RV (~2017 Final B7)4.3.5. Practice: Normal Approximation of a Binomial RV (~2016 Final B4c)
Mock Exam
Term Test 2 Overview
Course Notes
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