MAT 2379 Lecture Notes - Lecture 1: Osteoporosis, Biostatistics

• School: University of Ottawa
• Department: Mathematics
• Course: MAT 2379
• Professor: Maryam Sohrabi

Document Summary

We say that a and b are independent if. P (a b) = p (a)p (b) Remark: intuitively we would want independence of two events to mean the following. If a and b are independent, then the probability that a will occur should not depend on the fact that b has occurred or not. We will use this concept to generalize the concept of independence to more than two events. Let a1, a2, , an be a collection of events. We say that the events are independent if for any sub-collection ai1, ai2, , aik the following holds: P (ai1 ai2 aik) = p (ai1)p (ai2) p (aik) Mat 2379, introduction to biostatistics, lecture notes for chapter 5. Let a1, a2, , an be a collection of independent events. If we replace some of these events by their complement, for example replace ai with a(cid:48) i, then the new collection is still a collection of independent events.