Let Xn denote the capital of a gambler at the end of the nth play. His strategy

Question

Let Xn denote the capital of a gambler at the end of the nth play. His strategy is as follows. If his capital is 4 dollars or more, then he bets 2 dollars which earns him 4, 3, or 0 dollars with probabilities .25, .30 and .45. If his capital is 1,2 or 3 dollars then he bets 1 dollar which earns him 2 or 0 dollars with probabilities .55 and .45. When his capital become 0 he stops.

Let Yn be the net earnings in the nth play. That is Xn= Xn+1+ Yn
Compute P(Yn+1 = k|Xn =i) i=0,1,2,.....; k=-2,-1,0,1,2,.....

Explanation / Answer

Xn/Yn -2 -1 0 1 2 0 0 0 1 0 0 1 0 .45 0 .55 0 2 0 .45 0 .55 0 3 0 .45 0 .55 0 >4 .45 0 0 .30 .55

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.