This is for a Linear Algebra class. Please provide explanations for the answer (3) In the casino game of roulette, a ball is spun around a wheel with 38 slots, 18 of which are colored black. If you bet on black, then you gain a profit of $1 if the ball lands on one of the 18 black slots, but you lose $1 if it lands on one of the other 20 slots (a) Write out the transition matrix for a Markov Chain representing how much money you have in your pocket before and after a single play of roulette assuming that you will start with less than $10 and stop once you get to either $0 or $10. For example, if you have $4 at some point in the night, then you will either have $5 or S3 after the next round depending on whether black comes up or not, but if you get to $0 or $10 at any point, you stop playing (b) Calculate the eigenvalues of your transition matrix and identify all possible sta- tionary distributions. Discuss convergence (unique for any initial? fail to converge? etc. (c) Suppose that you start the night with S5. Calculate the probability that you double your money before losing it all (i.e. probability that you end the night with S10 instead of $0)

Question
This is for a Linear Algebra class. Please provide explanations for the answer
(3) In the casino game of roulette, a ball is spun around a wheel with 38 slots, 18 of which
are colored black. If you bet on black, then you gain a profit of $1 if the ball lands on
one of the 18 black slots, but you lose $1 if it lands on one of the other 20 slots
(a) Write out the transition matrix for a Markov Chain representing how much money
you have in your pocket before and after a single play of roulette assuming that
you will start with less than $10 and stop once you get to either $0 or $10. For
example, if you have $4 at some point in the night, then you will either have $5 or
S3 after the next round depending on whether black comes up or not, but if you
get to $0 or $10 at any point, you stop playing
(b) Calculate the eigenvalues of your transition matrix and identify all possible sta-
tionary distributions. Discuss convergence (unique for any initial? fail to converge?
etc.
(c) Suppose that you start the night with S5. Calculate the probability that you double
your money before losing it all (i.e. probability that you end the night with S10
instead of $0)
Expand
Transcribed Image Text

This is for a Linear Algebra class. Please provide explanations for the answer (3) In the casino game of roulette, a ball is spun around a wheel with 38 slots, 18 of which are colored black. If you bet on black, then you gain a profit of $1 if the ball lands on one of the 18 black slots, but you lose $1 if it lands on one of the other 20 slots (a) Write out the transition matrix for a Markov Chain representing how much money you have in your pocket before and after a single play of roulette assuming that you will start with less than $10 and stop once you get to either $0 or $10. For example, if you have $4 at some point in the night, then you will either have $5 or S3 after the next round depending on whether black comes up or not, but if you get to $0 or $10 at any point, you stop playing (b) Calculate the eigenvalues of your transition matrix and identify all possible sta- tionary distributions. Discuss convergence (unique for any initial? fail to converge? etc. (c) Suppose that you start the night with S5. Calculate the probability that you double your money before losing it all (i.e. probability that you end the night with S10 instead of $0)

Expert Answer

Want to see the step-by-step answer?

Check out a sample Q&A here.

Want to see this answer and more?

Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*

*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Tagged in
Math
Probability

Related Probability Q&A

Find answers to questions asked by students like you.

Q: For the experiment of rolling an ordinary pair of dice, find the probability that the sum will be od...

A: Concept of probability:Probability deals with the likelihood of occurrence of a given event. The pro...

Q: Of the plays attributed to a playwright, 17 are comedies, 16 are tragedies, and 20 are histories. If...

A: Plays attributed to playwright are as follows:17 are comedies , 16 are tragedies and 20 are historie...

Q: Hi, I would like to see the steps and explanations for question 3. Thank you!

A: Here it is given that X is continuously uniform distributed on [a,b]. The probability distribution f...

Q: About 30% of all recorded tsunamis have been nine meters or higher.† You are writing a report about ...

A: Note: In this question there are 5 parts and we are authorized to answer up to 3 subparts only, So w...

Q: A company is in the business of finding addresses of long-lost friends. The company claims to have a...

A: The distribution:The company claims to have 80% success rate. There are names of six friends for who...

Q: The probability density function of the time to failure of an electronic component in a copier (in h...

A: Computing the probability that a component fails in the interval from 465 to 1,943 hours:The random ...

Q: This is for a Linear Algebra class. Please provide answer including matrices since this is linear a...

A: Let x represent the intake of Annie's Organic Mac and Cheese , y represent the intake of Applegate's...

Q: A service has five tasks, performed in sequence.  In the instance when there is more than one worker...

A: Process capacity:For the entire process, the process capacity is given by the lowest number of flow ...

Q: Given P (A and B) 0 0.04, P (B) 0.64, P (B|A) 0.87, what is P (A)?

A: Conditional probability:The conditional probability describes that the probability of an event B occ...

Q: Suppose you are given the following (x, y) data pairs. x 1 2 6 y 4 3 9 Find the least-squa...

A: (a)Consider the given data and calculate the following:

Q: Use Bayes Theorem to calculate the probabilities: The enrollment in a certain course is 10% first ye...

A: Given probability of first year students enrolment in course P(F) = 0.10probability of sophmores enr...

Q: A total of 20 children, 14 men, and 12 women entered a raffle drawing. If the winner is randomly sel...

A: Total of men and women is given by 14+12=26Total of children, men and women is given by 20+14+12=46H...

Q: Question # 4 Consider a circular table with N > 4 seats. Chris and Sarah are two of N th at ests to ...

A: Given a circular table with N seats (N ≥4). Chris and Sarah are two among the N dinner guests,Let us...

Q: Two test parts are mixed in with a box of 25 good parts. Probability of randomly selecting one of th...

A: We have given a box of 25 good parts.Two test parts mixed with 25 good parts inside the boxSo,Total ...

Q: An urn contains five red balls and four white balls.  A sample of two balls is selected at random fr...

A: Concept of probability:Probability deals with the likelihood of occurrence of a given event. The pro...

Q: Haroldo, Xerxes, Regina, Shaindel, Murray, Norah, and Georgia are invited to a dinner party. They ar...

A: The total number of persons invited to dinner party = 7The total number of different possible order ...

Q: From the integers 1,2,3,4,5,6,7,8,9, two integers are randomly selected, determine the probability t...

A: Given integers: 1,2,3,4,5,6,7,8,9Now, we need to choose two integers from the above set. 

Q: If you roll a four sided die and a six sided dice ( numbered 1,2,3,4) what is the probability of rol...

A: Given a four sided dice which have numbers 1,2,3,4 and six sided dice have numbers 1,2,3,4,5,6 on it...

Q: Identify the following distribution as binomial, geometric or neither.A headache remedy is said to b...

A: In this question we have given some data based on that we have to find that which distribution is be...

Q: Given the following sampling distribution:X -18 -11 -4 4 19P(X) 7⁄100 1⁄50 9⁄100 1⁄20 ___(i) Find P(...

A: In this question we have given some probabilities at some values of x  and by using that information...

Q: A car dealership has 7 red, 14 silver, and 4 black cars on the lot. Ten cars are randomly chôsen to ...

A: We have given,A car dealership has 7 red, 14 silver & 4 black cars on the lotIf 10 cars are rand...

Q: A bag contains total 30 balls out of which 9 are red, 12 are white and 9 are blue. Two balls are dra...

A: Let us first find probability that the first ball is red. For that we will need the following.Since,...

Q: Let Xi be iid Exp(λ) random variables.1. Let Mn = max1≤i≤n Xi. Compute the CDF FMn (x).2. Using the ...

A: 1.Introduction:Here, X1, X2,,…, Xn, are iid (independent and identically distributed) random variabl...

Q: How many different five​-letter passwords can be formed from the letters A, B, C, D, E, F, G and H i...

A: Permutation rule:From a group of n items, k items can be arranged in ordered ways in,

Q: A single die is rolled one time. Find the probability of rolling a number greater than 5 or less tha...

A: Explanation:When a die is rolled once, the sample space of all possible outcomes is: {1, 2, 3, 4, 5,...

Q: The following table gives the total endothermic reactions involving sodium bicarbonate   Final T...

A: Note:Hi! Thank you for posting the question. However, from the given data, the problem was not compl...

Q: The letters A,H,I,M,O,T,U,V,W,X  and Y are all mirror images of themselfs. A string made of these le...

A: Given information:The letters A,H,I,M,O,T,U,V,W,X  and Y are all mirror images of themselfs. A strin...

Q: If a​ true-false test with 15 questions is​ given, what is the probability of scoring   ​(A) Exactly...

A: Introduction to binomial distribution:Consider a random experiment involving n independent trials, s...

Q: Use a truth table to determine whether this argument is valid or invalid: VALID INVALID p V q TITIT ...

A: The given arguments:The given symbolic form arguments and the argument (not yet verified whether cor...

Q: Thirty-three cards numbered from 1 through 33 are placed into a box and two cards are selected witho...

A: Given that thirty three cards are numbered from 1 to 33 and placed in a box.The total number of odd ...

Q: Let {1,2,3,4,5}A,{1,3,5,7,9}B,{ |0 11}Cxxisanevennaturalnumberbetweenand and {1,2,3,4,5,6,7,8,...

A:  Given A = {1,2,3,4,5},  B = {1,3,5,7,9} and C ={x}, where x is an even natural number between {0 an...

Q: On New Year's Eve, the probability of a person driving while intoxicated or having an accident is 0....

A: Given information:Denote the event “person driving while intoxicated” as A.The probability that a pe...

Q: Glven P (A)-0.56, P (B) - 0.75, P(C) = 0.12 and that events A, B, and C are independent, what is P (...

A: Independent events:If the probability of occurring of one event does not affect the probability of o...

Q: Hello, Please help me navigate this because I don't even know how tostart answering these questions ...

A: Hello there! I see that there are more number of questions on this graph. I can only help with first...

Q: If you draw five cards at random from a standard deck of 52 cards, what is the probability that ther...

A: Consider the provided problem: it is given that 5 cards are drawn from the deck of 52 cardsThe total...

Q: How many diffrent ways are there to distribute 12 identical bones among three diffrent dogs?

A: It is known that, for any equation,

Q: At a local car dealership, 100 people were injured during the end of year celebration event from tho...

A: Given that at the closing day, total people attended the event = 12500The total people got injured d...

Q: According to police sources, a car with a certain protection will be recovered 90% of the time. If 2...

A: Introduction:Consider the event of recovering a stolen car with the protection as a “success”.For a ...

Q: The flow in a river can be modeled as a log-normal distribution. From the data, it was estimated tha...

A: Let X be the flow in a river which follows log normal distribution.It is provided that, P(X > 821...

Q: Let N ∼ P oiss(λ) and let Xi be iid Ber(1/2) random variables that take on the values {0, 1} where P...

A: Compound probability distribution:Suppose X is a random variable that follows some probability distr...

Q: Use the Alternative formula for Variance to calculate the variance of the random variable in Table 1...

A: Find the mean of the random variable k using the given probability distribution.Discrete random vari...

Q: The state runs a lottery once every week in which six numbers are randomly selected from 17 without ...

A: Hyper geometric distribution:A hyper geometric distribution is a discrete probability distribution t...

Q: Assume that x has a normal distribution with the specified mean and standard deviation. Find the ind...

A: If a random variable x has a distribution with mean µ and standard deviation σ, then the z-score is ...

Q: According to national data, 20.7% of burglaries are cleared with arrests. A new detective is assigne...

A: In this question we are going to use Binomial Probability Distribution to get the probability. We ar...

Q: Quick Start Company makes 12-volt car batteries. After many years of product testing, the company kn...

A: If a random variable x has a distribution with mean µ and standard deviation σ, then the z-score is ...

Q: Show that for the simple random walk starting at zero,P(first visit to S^(2n) occurs at t = 2k) = P(...

A: Introduction:For a simple random walk starting at 0, denote Sn as a simple random walk of n steps. E...

Q: a bag of marbles has 8 green, 10 red, and 5 blue marbles. One marble is drawn from the bag. What is ...

A: For any event A, the probability of A for the sample space S, can be found as,

Q: Using A standard 52 card deck, you are dealt a five card poker hand. What is probability you will de...

A: Concept of probability:Probability deals with the likelihood of occurrence of a given event. The pro...

Q: The following problems refer to strings in A to Z.  (a) how many diffrent four letter strings are th...

A: In this question, we have to form a four letter strings using the letters A to Z.Since in this quest...

Q: What is the total revenue from music sales decreased from $14.6 billion to $5.5 billion between 2000...

A: If Revenue in  year 2000 was $14.6 Billion and Revenue in year 2014 was $5.5 billion. So the differe...