1. Chapter 3 & 4 Notes

2. 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

3. 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)

4. 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)

5. 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, ...