In Imaginationland, each person has exactly one child. Suppose that a child of a pro video...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
In Imaginationland, each person has exactly one child. Suppose that a child of a pro video gamer is also a pro video gamer with prob- ability 0.7, or an amateur video gamer with probability 0.3. Suppose that the child of an amateur video gamer is a pro video gamer with probability 0.1, or an amateur video gamer with probability 0.5, or a non-gamer with probability 0.4. Suppose that the child of a non- gamer is a pro video gamer with probability 0.1, or an amateur video gamer with probability 0.5, or a non-gamer with probability 0.4. (a) By drawing a suitable directed graph with probability edge-weights, model the described scenario as a three-state discrete-time Markov chain. (4 marks) (b) Write down the transition matrix P corresponding to the Markov chain that you drew in (a). (4 marks) (c) Based on your answer to (b), calculate the probability that the great grand-child of a non-gamer is a pro video gamer. (6 marks) (d) List the communication classes of the Markov chain that you drew in (a). For each communication class, determine with jus- tification whether it is recurrent or transient. Please state in full any relevant general results or definitions. (6 marks) (e) Compute, with justification, a stationary distribution for the Markov chain that you drew in (a). Is the stationary distribution unique? In the long run, what proportion of people in Imaginationland are pro video gamers? (5 marks) In Imaginationland, each person has exactly one child. Suppose that a child of a pro video gamer is also a pro video gamer with prob- ability 0.7, or an amateur video gamer with probability 0.3. Suppose that the child of an amateur video gamer is a pro video gamer with probability 0.1, or an amateur video gamer with probability 0.5, or a non-gamer with probability 0.4. Suppose that the child of a non- gamer is a pro video gamer with probability 0.1, or an amateur video gamer with probability 0.5, or a non-gamer with probability 0.4. (a) By drawing a suitable directed graph with probability edge-weights, model the described scenario as a three-state discrete-time Markov chain. (4 marks) (b) Write down the transition matrix P corresponding to the Markov chain that you drew in (a). (4 marks) (c) Based on your answer to (b), calculate the probability that the great grand-child of a non-gamer is a pro video gamer. (6 marks) (d) List the communication classes of the Markov chain that you drew in (a). For each communication class, determine with jus- tification whether it is recurrent or transient. Please state in full any relevant general results or definitions. (6 marks) (e) Compute, with justification, a stationary distribution for the Markov chain that you drew in (a). Is the stationary distribution unique? In the long run, what proportion of people in Imaginationland are pro video gamers? (5 marks)
Expert Answer:
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
(a) Prove by the Principle of Mathematical Induction that n > (2i 1) = n? i=1 (7 Marks) (b) Prove by contradiction that there are infinitely many prime numbers. (7 Marks) (c) Knowing that sequence...
-
Suppose that the joint density function for two continuous random variables X and Y is defined by fxx(r,y) = cry', if 0 < x, y < 1 fx.x (r, y) = 0, otherwise (a) Determine the value of c. (5 marks)...
-
An unfair coin has probability of landing heads. As an experiment, the coin is thrown repeatedly, until the first time it lands tails, after which the experiment ends. Suppose that this full...
-
Consider the following independent situations found during audit testing of Faran Ltd, which has a balance date of 30 June 2019. Assume that all the situations are material. (i)Recent industrial...
-
In a subway station, there are exactly enough customers on the platform to fill three trains. The arrival time of the nth train is X1+ + Xn where X1, X2 . . . are iid exponential random variables...
-
What are the pros and cons of having a third-party host and operate your Web site?
-
Heritage, a general contractor, had filed a breach of contract action against an electrical subcontracting firm that had withdrawn its bid right before the contract was to be performed. A jury had...
-
Mile-High Foods, Inc., was formed in March 2011 to provide prepackaged snack boxes for a new low cost regional airline beginning on April 1. The company has just leased warehouse space central to the...
-
As part of a survey, 15 adults were asked, "How many hours did you spend at your job last week?" The results are shown in the stem-and-leaf display below. Use the display to answer the questions that...
-
The following diagram is the original plan for a project. In reference to the diagram below answer the questions below. All durations are in weeks. DESIGN STRUCTURAL 37CCL 8.1 8.2 8.3 8.4 8.5 2...
-
The following table gives a partial list of Kenji's significant property (that is, although only the first three items are listed within each category, the totals at the bottom of the table include...
-
Balls 1, 2, 3, and 4 are hanging by strings. A plastic rod, which has been rubbed with wool, is used to touch Ball 1. When the balls are brought near each other, but not touching, the following is...
-
If A = (5.00 -7.00 ) units, B = (-7.00 +2.00 ) units, and C = (28.0 + 20.0 ) units, determine a and b such that a A+ bB + = 0. a = b = Need Help? Read It
-
The charge in the bottom right corner of the figure is Q = - 45 nC. What is the magnitude of the force on Q? 15 nC + 3 cm -5 nC 1 cm
-
Two identical small spheres of mass 1.02 g each carry equal charge (sign and magnitude) and are placed 3.7 cm apart. When released, each sphere experiences an instantaneous acceleration of 477 m/s2....
-
A simple pendulum consists of a point mass, m, attached to the end of a massless string of length L. It is pulled out of its straight-down equilibrium position by a small angle and released so that...
-
. When sketching y = CE(S, t) and y = PE(S, t), it was discovered that CE and PE have the same value at S = Er(T t). Derive this result by using the Put-Call Pariety Equation.
-
Identify Thank You mission, strategy and core competencies. Identify strategy changes that have taken place at Thank You since its founding in 2008. Your answer must in text references and must be...
-
What other possible organizations of the globin gene could exist if there were no need for a globin chaperone?
-
Will an amino acid be glucogenic or ketogenic if it is catabolized to the following molecules? (a) Phosphoenolpyruvate (b) a-Ketoglutarate (c) Succinyl-CoA (d) Acetyl-CoA (e) Oxaloacetate (f)...
-
People on high-fiber diets often have less cancer (especially of the colon) and lower blood-cholesterol levels than people on low-fiber diets, even though fiber is not digestible. Suggest reasons for...
-
In a(n)________ numbering system, all numeric values are written as sequences of 0s and 1s. a. hexadecimal b. binary c. octal d. decimal
-
What is a program?
-
List the five major components of a computer system.
Study smarter with the SolutionInn App