Conditional Probability (lec 2)

Question 1

What is P(B|A)

Answer 1

P(B|A) = P(A N B)/P(A)
P(A N B) = P(A) x P(B|A)

Question 2

What is multiplication principle (conditioning events)

Answer 2

Multiplication principle (conditioning events) is
P( i = 1 to n N Ai) = P(A1) x j=2 PI n P(Aj| k=1 N j-1 Ak) = P(A1) x P(A2|A1) x P(A3| A1 N A2)

Question 3

What is a partition

Answer 3

Partition is for all i, i in 1,…,n Hi N Hj = empty set and U I=1 to n Hi = omega.
Divide sample space into pairwise disjoint events

Question 4

What is law of total probability

Answer 4

Law of total probability is:
For all A in F, P(A) = sum i=1 to n P(A N Hi) = sum i=1 to n P(Hi) x (A|Hi)

Question 5

What does Bayes theorem state

Answer 5

Bayes theorem states that:
If H1,…,Hn is a partition of omega, for all A in F we have for all i
P(Hi|A) = (P(Hi)*P(A|Hi))/sum j=1 to n P(Hj)P(A|Hj)

Question 6

What is P(Hi|A)

Answer 6

P(Hi|A) = P(Hi N A)/P(A) = (P(Hi) x P(A|Hi))/P(A)