The Kolmogorov Axioms

Question 1

Probability measure

Answer 1

Let S be a sample space, P a set function.

P is a probability measure if the following axioms are satisfied:

• For any event E in S, P(E) >= 0
• P(S) = 1
• If E_1, E_2, …. are mutually exclusive, then P(E_1 union E_2 union… ) = Sum of P(E_i) where i = [0, infty)

Question 2

P(A^c)

Answer 2

P(A^c) = 1 - P(A)

Question 3

A intersection A^c

Answer 3

empty

Question 4

P(empty)

Answer 4

P(empty) = 0

Question 5

P(A intersection B^c)

Answer 5

P(A intersection B^c) = P(A) - P(A intersection B)

Question 6

If A subset B

Answer 6

If A subset B, then P(A) <= P(B)

Question 7

P(A union B)

Answer 7

P(A union​ B) = P(A) + P(B) - P(A intersection B)