Suppose a Markov % %% %% % % If the system starts in state 3, what is the probability that it goes to state 4 on the next observation, and then goes to state 2 on the following observation? (A) 4 (B) %4 (C) %4 (D) 16

Suppose a Markov % %% %% % % If the system starts in state 3, what is the probability that it goes to state 4 on the next observation, and then goes to state 2 on the following observation? (A) 4 (B) %4 (C) %4 (D) 16

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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Suppose we are interested in investing in one of three investment opportunities: d1, d2, or d3. The following profit payoff table shows the profits (in thousands of dollars) under each of the 3 possible economic conditions: s1, s2, and s3 Assume the states of nature have the following probabilities: P(s1) = 0.2, P(s2) = 0.3, P(s3) = 0.5. Which decision alternative is best?
A certain system can experience three different types of defects. Let A; (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A₂) = 0.10 P(A3) = = 0.07 P(A₁ U A3) = 0.18 P(A₁ A₂ A3) = 0.02 = 0.15 P(A₁) = P(A₁ U A₂) = 0.17 P(A₂ U A3) = 0.13 (a) What is the probability that the system does not have a type 1 defect? (b) What is the probability that the system has both type 1 and type 2 defects? (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (d) What is the probability that the system has at most two of these defects?
Bob, the proprietor of Midway Lumber, bases his projections for the annual revenues of the company on the performance of the housing market. He rates the performance of the market as very strong, strong, normal, weak, or very weak. For the next year, Bob estimates that the probabilities for these outcomes are 0.15, 0.23, 0.41, 0.10, and 0.11, respectively. He also thinks that the revenues corresponding to these outcomes are $25, $18.5, $16.8, $14, and $13 million, respectively. What is Bob's expected revenue for next year? (Round your answer to two decimal places.)$ million
The cola market is controlled by two firms, Cola 1 and Cola 2. As a market analyst, you have been provided with the following information: (1) Current Cola 1 drinkers will drink Cola 1 the next time they purchase cola with probability 0.8; (ii) Current Cola 2 drinkers will drink Cola 2 the next time they purchase cola with probability x, where 0.5 < x < 1; (iii) over a long period of time, a cola drinker will purchase Cola 2 with frequency Make the following assumptions: (i) the cola market is in steady state; (ii) all cola drinkers display the same stochastic behaviour. Based on the information provided, what is the value of x?
A certain system can experience three different types of defects. Let A, (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A,) = 0.15 P(A, U A2) = 0.16 P(A2 U A3) = 0.12 P(A2) = 0.09 P(A, U A3) = 0.17 P(A, n A2 n A3) = 0.02 P(A,) = 0.06 .(a).What.is.the probability that the system does not have a type 1 defect? Enter a number. (b) What is the probability that the system has both type 1 and type 2 defects? (c) What is the probability that the system has both type 1 and type 2 defects but not a type 3 defect? (d) What is the probability that the system has at most two of these defects?
Suppose a distribution center is considering three options for expansion. The first one is to expand into a new plant, the second to add on third-shift to the daily schedule, and third, a small expansion to the existing facility. There are three possibilities for demand. These are high, medium, and low having probabilities of 40%, 33%, and 27% respectively. Suppose that the profits for the expansion plans are as follows: The new plant expected outcomes are $110,000, $50,000, -$15,000, the third shift consideration would result in outcomes of $40,000, $20,000, $-5,000 and the small expansion choice would in the following dollar amounts $15,000, $13,000, -$1,500. The amount that the company must invest in each alternative is: new plant = $48,000, third shift = $15,100, small expansion = $8,700 a. The profit/loss (EMV) for the new plant is $ [Select] b. The profit/loss (EMV) for adding a third shift is $ [Select] c. The profit/loss (EMV) for the small expansion is $ [Select] d. Which of…
Assume that a website www.funwithmath1600.ag has three pages: • Page A: King Algebra • Page B: Learn1600andWin Page C: Linear AlgbraIsEverywhere Each page has some links to the other pages of this website and no pages links to any page outside this website. • Page A has three links to page B and only one link to page C. • Page B has three links to page A and two links to page C. • Page C has one link to page A and two links to page B. A student decides to explore this website starting from page A. Since reading content is always a boring task (is it?!) they decide to choose one of the links in page A with equal probability and click on the link to see the next page. As a result, on the next step, they will end up on page B with probability 3/4 and on the page C with probability 1/4. This process is then continued by the student with the same rule: Go the next page by clicking, with equal probability, on one of the existing links that are on the present page. (Use only fractions in your…
2. This year Karen has decided to diversify her business by growing broc- coli as well as lettuce. Karen plants lettuce with a probability of or broccoli with a probability of . By the time these plants are ready to harvest the price of lettuce increases with a probability of and decreases with a probability of 3. The price of broccoli increases with a probability of , decreases with a probability of or stays the same with a probability of . (a) Draw a probability tree for this scenario. (b) Use the probability tree to determine the probability that Karen plants broccoli and that the price of broccoli increases by the time it is ready to harvest. (c) Use the probability tree to determine the probability that the price of whatever Karen plants increases by the time it is ready to harvest. (d) Calculate Pr(Price of lettuce does not change | Karen plants lettuce). (e) Calculate Pr(Price of broccoli does not changen Karen plants broccoli).
A certain system can experience three different types of defects. Let Ai (i = 1,2,3) denote the event that the system has a defect of type i. Suppose that the following probabilities are true. P(A1) = 0.10 P(A2) = 0.07 P(A3) = 0.06P(A1 ∪ A2) = 0.11 P(A1 ∪ A3) = 0.13P(A2 ∪ A3) = 0.11 P(A1 ∩ A2 ∩ A3) = 0.01 (c) Given that the system has at least one type of defect, what is the probability that it has exactly one type of defect? (Round your answer to four decimal places.) (d) Given that the system has both of the first two types of defects, what is the probability that it does not have the third type of defect? (Round your answer to four decimal places.)
The following is a payoff matrix for a 4x4 game between A (column player and B (row player). What is the expected value of this game if both players picked their (row or column) at random? -3 4 1 -2 -2 -3 4 1 1-2 -3 4 4 1-2 -3
(Devore: Section 2.4 #59) At a certain gas station, 40% of the customers use regular gas (A₁), 35% use plus gas (A₂), and 25% use premium A3. Of those customers using regular gas, only 30% fill their tanks (event B). Of those customers using plus, 60% fill their tanks, whereas of those using premium, 50% fill their tanks. (a) What is the probability that the next customer will request plus gas and fill the tank (A₂B)? (b) What is the probability that the next customer fills the tank? (c) If the next customer fills the tank, what is the probability that regular gas is requested? Plus? Premium?