9/2/2020

Discussion of R code to simulate Pi - volunteers

Probability (Review)

• Basic Axioms
• Relative frequence interpretation of P(A)
• Addition rule for disjoint events: P(AUB) = P(A) + P(B), if A and B are disjoint
• General addition rule: P(A or B)=P(A) + P(B) - P(A and B)
• Countable versus uncountable sets
• Different probability measures on the same set
• Counting: permutations versus combinations
• Conditional probability: P(A|B) = P(A and B)/P(B)
• Multiplication rule: P(A and B) = P(A|B)P(B) = P(B|A)P(A)
• Independence: P(A|B) = P(A)
• Multiplication rule for independent events: P(A and B) = P(A) x P(B)
• Law of Total Probability
• Bayes Theorem

Class Exercises/Activity

• 14.27 and 14.28 on p. 283 (Exercise 5.10 on p. 85 may be helpful for generating binary sequences)

Please complete your reading of Chapter 14 and begin reading Chapter 15 Random Variables for class on Friday

• We will have our first problem session on Friday. If we finish the exercises, then we will begin the material in Chapter 15.