Two people A and B play a series of games, in which they bet on aparticular share price increasing or decreasing on a particular day. Ifthe share price increases, player B pays player A £1; whereas if theshare price decreases, player A pays player B £1. The probabilityof the share price increasing on any particular day is p independentlyof any other day, and the probability of the share price decreasing isq = (1– p). Initially, both A and B have £2, and the series of gamesends when one player runs out of money. We let X, be amount ofmoney possessed by player A after n days, so Xo = 2, and we considerthe random process Xo, X1, X2, ....(a) Explain why the state space of this random process is {0, 1, 2, 3, 4}.(b) Explain why this random process is a Markov process.(c) Explain why the transition matrix for this random process is1 0 0 0 0q 0 p 0 00 0 q 0 p0 0 0 0 1(d) What is the 2-step transition matrix for this Markov process?(e) Classify the states of this random process.

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Answered: Two people A and B play a series of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A investment company has an asset A that will produce a cash flow of $5.500 with prob. 0.3 and $8,800 with prob. 0.7. They also own an asset B that pays $1,550 with prob. 0.5 and $3.500 with prob. 0.50. In this case, the probability that the company will earn a total payoff of $10,350 from their portfolio of assets is and the expected value of this portfolio is_ O a15: $10.335 O 0.15: $10885 O 035: $1088S O 035, $10.33s
Charlie buys a one-year term home insurance policy for $p, that will pay $200,000 in the event of a major catastrophe and $35,000 in the event of a minor catastrophe. Charlie's home has a 0.2% chance of a major catastrophe and a 0.7% of a minor catastrophe during the one year term. What did the insurance company charge Charlie for this policy if the company expected to break even?
José plays basketball. He makes free throw shots 43% of the time. José must now attempt two free throws. The probability that José makes the second free throw given that he made the first is 0.49. Is José's first free throw shot independent of his second free throw shot? There is not enough information to determine whether or not the two free throws are independent of each other. The two free throws are dependent on each other. O The two free throws are independent of each other. What is the probability that José makes both free throws? Round your answer to three decimal places.
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A investor estimates that, in a year’s time, a certain stock has a 30% chance to be worth $125 per share, a 45% chance to be worth $90 per share, and a 25% chance to be worth$60 per share. Determine the expectation of the price per share of the stock in a year’s time.
You purchase a brand new car for $15,000 and insure it. The policy pays 78% of the car's value if there is an issue with the engine or 30% of the car's value if there is an issue with the speaker system. The probability of an issue with the engine is 0.009, and the probability there is an issue with the speaker system is 0.02. The premium for the policy is p. Let X be the insurance company's net gain from this policy. (a) Create a probability distribution for X, using p to represent the premium on the policy. Enter the possible values of X in ascending order from left to right. P(X) (b) Compute the minimum amount the insurance company will charge for this policy. Round your answer to the nearest cent
Q6
The proprietor of Midland Construction Company has to decide between two projects. He estimates that the first project will yield a profit of $160,000 with a probability of 0.7 or a profit of $120,000 with a probability of 0.3; the second project will yield a profit of $220,000 with a probability of 0.6 or a profit of $70,000 with a probability of 0.4.Find the expected profit for each project. first project $ second project $ Which project should the proprietor choose if he wants to maximize his expected profit? first project second project
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EXAMPLE 32. The probability that a contractor will get a plumbing contract is 2/3, and the probability that he will not get an electric contract is 5/9, the probability of getting at least one contract is 4/5, what is the probability that he will get both ?

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