3) At time 0, Elon Musk (the cool guy these days) has $2. At times 1, 2,..., heindependently plays a game in which he bets $1. With probability p = 0.49, he wins the game and withprobability 1 - p = 0.51, he loses the game. His goal is to increase his capital to $3, and as soon as hedoes, the game is over. The game is also over if his capital is reduced to zero. Construct an absorbingMarkov chain and answer the following questions.• What is the expected duration of the game?• What is the probability that he goes broke?

Answered: Image /qna-images/answer/f321e7aa-5f42-4e89-bd59-ce438abeb7fe.jpg

Answered: 3) At time 0, Elon Musk (the cool guy…

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 customer has approached a bank for a $100,000 one-year loan at an 8% interest rate. If the bank does not approve this loan application, the $100,000 will be invested in bonds that earn a 6% annual return. Withoutadditional information, the bank believes that there is a 4% chance that this customer will default on the loan, assuming that the loan is approved. If the customer defaults on the loan, the bank will lose $100,000. At a cost of $1000, the bank can thoroughly investigate the customer’s credit record and supply a favorable or unfavorable recommendation. Past experience indicates that the probability of a favorable recommendation for a customer who will eventually not default is 0.80, and the chance of a favorable recommendation for a customer who will eventually default is 0.15.a. Use a decision tree to find the strategy the bank should follow to maximize its expected profit.b. Calculate and interpret the expected value of information (EVI) for this decision problem.c.…
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
Suppose you toss a coin and will win $5 if it comes up heads. If it comes up tails, you toss again. This time you will receive $10 if it comes up heads. If it comes up tails, toss again. This time you will receive $20 if it is heads and nothing if it comes up tails. What is the mathematical expectation for this game? What is the expectation for the $1 bets on a U.S. roulette wheel? See the figure. (Round your answer to the nearest cent.) Six-number bet
You flip two fair coins. If both coins land heads you win $2. Otherwise you lose $1. What is the expectation of this game? Round your answer to the nearest cent.
The St. Petersburg paradox is a coin flip game, where a fair coin is tossed successively, until heads occurs. If the first toss is heads, you win $1. If the first one is tails and the second one is heads, you win $2. If the first heads occurs in the third toss, you win $4 and so forth. The amount of money you win is doubled with each coin flip you survive. In the eighteenth century it was believed that the fair price for participating in such a game would be the expected wealth you gain. Show that the expectation value of the St. Petersburg game is infinite.
solve question 2 pppllleeaaaasee
If the famous insurance company, Lloyd’s of London, insures a $3 million Monet painting for $5000 per year. And, in each year, the painting has a .00021 chance of being stolen according to the Lloyd’s research team? From Lloyd’s perspective, find the expectation for insuring this painting for one year
Leah is flying from Moncton to Vancouver with connection in Montreal. The proba- bility that her first flight leaves on time is 0.15. If the flight is on time, the probability that her luggage will make the connecting flight in Montreal is 0.95, but if the first is Practice q # 25 p.197 delayed, the probability that the luggage will make it is only 0.65. chap 7 Are the first flight leaving on time and the luggage making the connection independent events? Explain. What is the probability that Leah's luggage arrives in Vancouver with a. b. her?
4. Claire is considering investing in a new business. In the first year, there is a probability of 0.2 that the new business will lose $10,000, a probability of 0.4 that the new business will break even ($0 loss or gain), a probability of 0.3 that the new business will make $5,000 in profits, and a probability of 0.1 that the new business will make $8,000 in profits. a. Claire should invest in the company if she makes a profit. Should she invest? Explain using expected values. b. If Claire's initial investment is $1,200 and the expected value for the new business stays constant, how many years will it take for her to earn back her initial investment?
Suppose it costs $29 to roll a pair of dice. You get paid 4 dollars times the sum of the numbers that appear on the dice. What is the expected payoff of the game? Is it a fair game? The expected payoff of the game is $? is it a fair game?
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You are planning to place a bet on your local sports team, the Red Sparrows. The Sparrow's have a past record of 4-5 (4 wins, 5 losses) at this venue. However you also know that their record is 2-7 in games where it rains and it has rained at 60% of their games this season. 4 If the Red Sparrows win their game what is the probability that it rained at that game?

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