Gamblers Ruin 2

Question 1

What is conditional expectation of X given B

Answer 1

Conditional expectation of X given B is
E[X|B] = E[X ; B]/ P(B)

Question 2

What is E[X;B) (X and B)

Answer 2

E[X;B] is E[X1B] = integral over B X(w)*dP(w)

Question 3

How can be split E(X) relative to B

Answer 3

Can split E(X) relative to B by:
E(X) = E(X(1B + 1B^C)) = P(B)E(X|B) + P(B^C)E(X|B^C)

Question 4

Study notes for gamblers ruin

Answer 4

Study notes for gamblers ruin