8/28/2017

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 - modify or write R code to estimate Pi

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

Please read Chapter 15 Random Variables for class on Wednesday