9/6/2023

Chapter 2 - Conditional Probaility and Independence

• Solutions to the Bayes examples on the handout
• Questions on your reading from Chapter 2
  • General multiplication rule - see p. 52
  • Bayes Rule - see p. 67
  • Independence
• In class exercises
  • Consider a sample space S of 5 outcomes {w1, w2, w3, w4, and w5} with probabilities P(w1)=1/8, P(w2)=P(w3)=P(w4)=3/16. Let A={w1, w2, w3} and B={w1, w2, w4} and C={w1, w3, w4}.
    • Show that P(ABC)=P(A) x P(B) x P(C), but that A, B, and C are not pairwise independent.
  • Show that if A, B, C, and D are independent, then AB and CUD are independent.
  • Prove the inclusion-exclusion formula for n events.

Please read Sections 3.1 through 3.4 for class on Monday. Our next Problem Session will be on Friday.