Homework Answers
Add Answer to:
1 Modify the gambler's ruin problem so that the probability of winning isp, losing is q...
Suppose in the gambler's ruin problem that the probability of winning a bet de- pends on the gambler's present fortune. Specifically, suppose that ai is the prob- ability that the gambler win...
Suppose in the gambler's ruin problem that the probability of winning a bet de- pends on the gambler's present fortune. Specifically, suppose that ai is the prob- ability that the gambler wins a bet when his or her fortune is i. Given that the gambler's initial fortune is i, let P(i) denote the probability that the gambler's fortune reaches N before 0. (a) Derive a formula that relates Pi) to Pi -1 and Pi 1) (b) Using the same approach...
B2. Describe the basic ideas behind the gambler's ruin model. For an unfair game where the...
B2. Describe the basic ideas behind the gambler's ruin model. For an unfair game where the gambler has probability p of winning and q (1-p) of losing, show that the probability that the gambler attains a fortune of N starting from an initial sum of j is given by 1-(a/p) obtain a similar expression for φ, the probability that, starting from €, the gambler is ruined before reaching EN and show that dj+ ,-1 for all j 0,1, ,N. Explain...
Exercise 7.1 (Gamblers ruin). Let (Xt) 120 be the Gambler's chain on state space Ω =...
Exercise 7.1 (Gamblers ruin). Let (Xt) 120 be the Gambler's chain on state space Ω = {0, 1,2, , N} (i) Show that any distribution r-[a,0,0, ,0, bl on 2 is stationary with respect to the gambler?s (ii) Clearly the gambler's chain eventually visits state 0 or N, and stays at that boundary state introduced in Example 1.1. chain. Also show that any stationary distribution of this chain should be of this form. thereafter. This is called absorbtion. Let Ti...
1. Consider the following "Gambler's Ruin" problem. A gambler starts with a certain number of dol...
1. Consider the following "Gambler's Ruin" problem. A gambler starts with a certain number of dollar bills between 1 and 5. During each turn of the game, there is a .55 chance that the gambler wil win a dollar, and a .45 chance that the gamble will lose a dollar. The game ends when the gambler has either S0 or S6. Let Xn represent the amount of money that the gambler has after turn n. (a) Give the one-step transition...
Question 8 10 pts In a casino game based on the standard gambler's ruin problem, the...
Question 8 10 pts In a casino game based on the standard gambler's ruin problem, the gambler and the dealer each start with 20 tokens. One token is bet on at each play. The game continues until one player has no further tokens. It is decreed that the probability that any gambler is ruined is 0.55 to protect the casino's profit. What should the probability that the gambler wins at each play be? Give your answer to 4 decimal places.
1.5, Consider a gambler's ruin chain with N 4. That is, if 1 i 3, p(i,i...
1.5, Consider a gambler's ruin chain with N 4. That is, if 1 i 3, p(i,i + - 0.4, and p(i,i -1) 0.6, but the endpoints are absorbing states: p(0, 0)1 and p(4 , 4-1 Compute p3 (1, 4) and p3 (1,0)
Problem 5: Gambler's Ruin Our old friend John Doe who tried his luck at blackjack back in Homework 2 now decides to win a small fortune using slot machines mstead. Having ganed some wisdom from h...
Problem 5: Gambler's Ruin Our old friend John Doe who tried his luck at blackjack back in Homework 2 now decides to win a small fortune using slot machines mstead. Having ganed some wisdom from his previous outings, he starts off small with just one dollar. He plays the slot machines in the following way He always inserts one dollar into the slot machines After playing it, the machine returns two dollars with probability p and returns nothing with probability...
Gambler’s Ruin. A gambler, player A, plays a sequence of games against an opponent, player B....
Gambler’s Ruin. A gambler, player A, plays a sequence of games against an opponent, player B. In each game, the probability of player A winning is p. If player A wins, he wins $1 which is paid by player B. If he loses a hand with probability q = 1-p, he must pay $1 to player B. The game ends either player B wins all the money from player A, and he is “ruined,” or when player A wins all...
Simulate a code through matlab the following problem. A random walk with P(X_n = i+1 |...
Simulate a code through matlab the following problem. A random walk with P(X_n = i+1 | X_{n-1} = i) = .4, and P(X_n = i-1 | X_{n-1} = i) = .6. Find the mean and variance of the number of transitions needed to get from state 5 to state 0. Find the probability you reach 10 before you reach 0 starting from 5. Check this with the formula from the gambler's ruin problem.
In a game, you have a 1/28 probability of winning 125 dollars and a 27/28 probability...
In a game, you have a 1/28 probability of winning 125 dollars and a 27/28 probability of losing 5 dollars. ON AVERAGE, how much would you expect to win or loose playing this game? SELECT ALL APPLICABLE CHOICES A) E=−23.7E=−23.7 B) E=−0.357E=−0.357 C) E=12.3E=12.3 D) E=−20.4
Suppose in the gambler's ruin problem that the probability of winning a bet de- pends on the gambler's present fortune. Specifically, suppose that ai is the prob- ability that the gambler wins a bet when his or her fortune is i. Given that the gambler's initial fortune is i, let P(i) denote the probability that the gambler's fortune reaches N before 0. (a) Derive a formula that relates Pi) to Pi -1 and Pi 1) (b) Using the same approach...
B2. Describe the basic ideas behind the gambler's ruin model. For an unfair game where the gambler has probability p of winning and q (1-p) of losing, show that the probability that the gambler attains a fortune of N starting from an initial sum of j is given by 1-(a/p) obtain a similar expression for φ, the probability that, starting from €, the gambler is ruined before reaching EN and show that dj+ ,-1 for all j 0,1, ,N. Explain...
Exercise 7.1 (Gamblers ruin). Let (Xt) 120 be the Gambler's chain on state space Ω = {0, 1,2, , N} (i) Show that any distribution r-[a,0,0, ,0, bl on 2 is stationary with respect to the gambler?s (ii) Clearly the gambler's chain eventually visits state 0 or N, and stays at that boundary state introduced in Example 1.1. chain. Also show that any stationary distribution of this chain should be of this form. thereafter. This is called absorbtion. Let Ti...
1. Consider the following "Gambler's Ruin" problem. A gambler starts with a certain number of dollar bills between 1 and 5. During each turn of the game, there is a .55 chance that the gambler wil win a dollar, and a .45 chance that the gamble will lose a dollar. The game ends when the gambler has either S0 or S6. Let Xn represent the amount of money that the gambler has after turn n. (a) Give the one-step transition...
Question 8 10 pts In a casino game based on the standard gambler's ruin problem, the gambler and the dealer each start with 20 tokens. One token is bet on at each play. The game continues until one player has no further tokens. It is decreed that the probability that any gambler is ruined is 0.55 to protect the casino's profit. What should the probability that the gambler wins at each play be? Give your answer to 4 decimal places.
1.5, Consider a gambler's ruin chain with N 4. That is, if 1 i 3, p(i,i + - 0.4, and p(i,i -1) 0.6, but the endpoints are absorbing states: p(0, 0)1 and p(4 , 4-1 Compute p3 (1, 4) and p3 (1,0)
Problem 5: Gambler's Ruin Our old friend John Doe who tried his luck at blackjack back in Homework 2 now decides to win a small fortune using slot machines mstead. Having ganed some wisdom from his previous outings, he starts off small with just one dollar. He plays the slot machines in the following way He always inserts one dollar into the slot machines After playing it, the machine returns two dollars with probability p and returns nothing with probability...
Most questions answered within 3 hours.
-
Describe the difference between a Change Order (CO), a
Request For Information (RFI), and submittals? Give...
asked 3 minutes ago -
A researcher claims that at least 10% of young children suffer
from some food allergy. A...
asked 4 minutes ago -
Help
can you do this?
C programming
Overview
In this program, you will be taking product...
asked 17 minutes ago -
The given plaintext is “Feistel
cipher structure uses the same algorithm for both encryption and
decryption”....
asked 21 minutes ago -
Use the redox table below to answer the following questions.
a) Would MnO2 reduce Cu2+?
b)...
asked 33 minutes ago -
import java.util.Scanner;
public class SieveOfEratosthenes {
public static void main(String args[]) {
Scanner sc...
asked 27 minutes ago -
Given the data below for the reaction, 2 A + 2 B + 4 C =>...
asked 33 minutes ago -
What were the sources of Spanish power in these centuries? Why
was Spain unable to sustain...
asked 35 minutes ago -
How do primary producer, primary consumers, secondary consumers,
and tertiary consumers affect the environment ?
asked 40 minutes ago -
The pet industry has undergone a surge in recent years,
surpassing even the $20 billion a...
asked 49 minutes ago -
what will be a good equation in order to find the
angular torque of the extension...
asked 52 minutes ago -
One of your friends wears glasses with a focal length of 44 cm .
Assume that...
asked 57 minutes ago