Chapter 3 & 4 Notes

Conditional Probability P(A|B) P(A|B) is read, “the probability of A given B” B is known to occur. P(A|B) = P(A  B) / P(B), if P(B) > 0 i.e. the conditional probability is the probability that both occur divided by what is given occurs

The multiplication rule and  intersectionmultiply P(A  B) = P(A)*P(B|A) = P(B)*P(A|B) (Note that this is an algebraic manipulation of the formula for conditional probability.) Intersections get more complicated when there are more events, e.g. P(ABCD) = P(A)* P(B|A)*P(C|AB)*P(D|A BC)

Independent Events A and B are independent if any of the following are true: P(AB) = P(A)*P(B) P(A|B) = P(A) P(B|A) = P(B) You need to check probabilities to determine if events are independent. If A, B, C, & D are pairwise independent, P (AB C D) = P(A)*P(B)*P(C)*P(D)

Ch 4 Topics Define random variable (discrete/continuous) probability mass function cumulative distribution function expected value Binomial Random Variable p(x)=C(n,r)p^x*q^(n-x) x=0,1,2,…,n Geometric Random Variable p(x)=q^(x-1)*q x = 1,2, 3, ...