STAT 2230 Lecture Notes - Lecture 3: Sample Space, Random Variable, Venn Diagram

• School: University of Guelph
• Department: Statistics
• Course: STAT 2230
• Professor: Bill White

Document Summary

If yes, then dependent and use conditional probabilities. If no, then independent and can use multiplication rule. Mutually exclusive/disjoint events: they have no outcomes in common and can never occur together. For any event a, p(a does not occur)=1-p(a) Both events can occur at the same time. To determine if something happens multiple times in a row a certain number of times, p(e1, e2, e3 and e4)=p(e1)x p(e2)x. P(a|b)=probability of event a occurring assuming b occurs. P(a and b)=p(b) x p(a|b) where p(b|a)=p(a and b)/p(b) Numerical outcome for a random phenomenon (has to be quantitative) If all conditions are satisfied, we can use the binomial formula. Have a fixed number of trials or observations. Outcomes in two categories (either success or failure) If x fits the binomial model: mean=np variance=npq. Probabilities represented by heights of bars in a density histogram. Fixed number of trials, success or failure, same probability of outcome each time, srs are conditions.