Question

8.4 Gambling Game

Dafna starts out with zero dollars. Every day she gains a dollar with probability p, stays put with probability s, or loses all her money (goes broke) with probability b, where p + s + b =1. Dafna plays the game forever. Use a DTMC to determine the stationary probability that Dafna has i dollars. What happens to your solution when s =0? What is Dafna’s long-run expected money?

Answer 1

S+ 2 babi lities eb aollas hespe State balance equateng T +T+ Tp TTo

TTo bt.ト ne ト(b+ト) t- P