Week 2

Question 1

Explain the notation P(A|B)?

Answer 1

Posterior probability - “after given new information”.

The conditional (updated) probability of A, given B occurs.

Question 2

What is the formula for conditional probability?

Answer 2

P (A|B) = P (A n B) / P (B)

P (B) > 0

Question 3

What is the Product Rule?

Answer 3

P(A1 n … n An) = P(A1)P(A2|A1) … P(An | A1 n … n An-1)

Question 4

What is the Law of Total Probability?

Answer 4

P(A) = P(A|B)P(B) + P(A|Bc)P(Bc)

Question 5

What is Bayes’ Formula?

Answer 5

P(B|A) = P(A|B)P(B) / P(A|B)P(B) + P(A|Bc)P(Bc)

P(B) = likelihood of cause
P(A|B) = probability of effect given cause

Question 6

When can we say two events are independent?

Answer 6

P(A n B) = P(A)P(B)

P(A|B) = P(A)

Question 7

When are events pairwise independent?

Answer 7

P(A n B) = P(A)P(B)
P(B n C) = P(B)P(C)
P(C n A) = P(C)P(A)

Question 8

When are events mutually independent?

Answer 8

When they are pairwise independent and P(A n B n C) = P(A)P(B)P(C).