Find an expression of the form E an that represents the total expected number of transactions n=1 where one of the fake bills are successfully used without being detected. Then determine if converges or diverges, and find its sum, if possible. your series

Find an expression of the form E an that represents the total expected number of transactions n=1 where one of the fake bills are successfully used without being detected. Then determine if converges or diverges, and find its sum, if possible. your series

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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1. A certain stock price has been observed to follow a pattern. If the stock price goes up one day, there's a 20% chance of it rising tomorrow, a 30% chance of it falling, and a 50% chance of it remaining the same. If the stock price falls one day, there's a 35% chance of it rising tomorrow, a 50% chance of it falling, and a 15% chance of it remaining the same. Finally, if the price is stable on one day, then it has a 50-50 change of rising or falling the next day. Which matrix below is the transition matrix for this Markov chain, if we list states in the order: (rising, falling, constant). 20 30 50 35 50 15 50 50 0 ). 0.2 0.35 0.5 0.3 0.5 0.5 0.5 0.15 20 35 50 30 50 50 50 15 0 0.2 0.3 0.5 0.35 0.5 0.15 0.5 0.5 2. Choose the correct transition matrix representing the Markov chain with state diagram shown below. Assume the states are ordered with A before B. 0.13 0.87 0.09 В 0.91 0.13 0.87 0.91 0.09 0.13 0.91 0.87 0.09 0.13 0.87 0.09 0.91 0.87 0.09 0.13 0.91 3. Given the initial state…
8. Individual Problems 20-4 Suppose that every driver faces a 4% probability of an automobile accident every year. An accident will, on average, cost each driver $5,000. Suppose there are two types of individuals: those with $30,000.00 in the bank and those with $2,500.00 in the bank. Assume that individuals with $2,500.00 in the bank declare bankruptcy if they get in an accident. In bankruptcy, creditors receive only what individuals have in the bank. Assume that both types of individuals are only slightly risk averse. In this scenario, the actuarially fair price of full insurance, in which all damages are paid by the insurance company, is $ Assume that the price of insurance is set at the actuarially fair price. At this price, drivers with $30,000.00 in the bank likely v buy insurance, and those with $2,500.00 in the bank likely buy insurance. (Hint: For each type driver, compare the price of insurance to the expected cost without insurance.) Suppose a state law has been passed…
A particular gambling game pays 4 to 1 and has a 20% chance to win. Someone will bet $10, 125 times, and keep track of the total amount won or lost. Which of the following boxes will produce the right answers? Check ALL answers that apply. a. 1 ticket labeled $10 and 4 tickets labeled -$10 b. 20 tickets labeled $10 and 80 tickets labeled -$10 c. 20 tickets labeled 1 and 80 tickets labeled 0 d. 1 ticket labeled $40 and 4 tickets labeled -$10 e. 20 tickets labeled $40 and 80 tickets labeled -$10 f. 1 ticket labeled 1 and 4 tickets labeled 0
There are X-Mart and Y-Mart convenience stores. It is assumed that each customer purchases once a week at one of the two supermarkets (but not both). In a study, a sample of 100 buyers was taken for 10 weeks. From this research it is known that if buyers go to X-mart store one week, 85 people will still buy at X-mart store the following week and if buyers go to Y-mart store one week, 70 people will still buy at Y-mart store. mart the following week. 1. Make a table and matrix of transition probabilities. 2. If John purchases at X-mart in the first week, what is the probability that Bob purchases at X-store in the third and fourth weeks?
Solve the following problem, similar to problem 4 from section 2.4 of your text. You select 9 cards randomly from a deck of 52 cards. What is the probability that all of the cards selected are face cards (i.e. jacks, queens, or kings)?
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Could you do Problem 11, questions a, b, and c?