John and his brother play a game as following: John tosses a biased die, and he

Question

John and his brother play a game as following: John tosses a biased die, and he asks his brother to guess the outcome before each toss. If the outcome is bigger than the guess, John will win; if the outcome is less than the guess, his brother will win; if they are equal, no one will win. The game ends when one of them wins. Suppose that on each toss the probability John wins is p, his brother wins is q, and no one wins is 1 - p - q. Let N be the number of times John has to toss until the game ends. Find its PMF and E[N], Var(N)?

Explanation / Answer

probabilty that game ends on Nth toss =P(till N-1 game no body wins )*somebody wins on Nth term

=(1-p-q)N-1*(p+q)

this is a sort of geomteric distribution were probabilty for termination of game =(p+q) when somebody wins

hence E(N) =1/(p+q)

and Var(N) =(1-p-q)/(p+q)2

Related Questions

Navigate

• Browse (All)
• Browse J
• Subjects

---

---

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