9.A naturalist is observing the behavior of a frog in a smalllily pond. There are four lily pads in the pond, and the frogjumps from one to another. The pads are numbered arbitrarily;the state of the system is the number of the pad that the frog is on.Transitions occur only when he jumps. Although he can jumpfrom any pad to any other, the probability of jumping to anygiven pad from the one he is on is inversely proportional to thedistance (that is, he is more likely to jump to a near pad than a farone). The distances areBetween lily pads 1 and 2Between lily pads 1 and 3Between lily pads 1 and 4Between lily pads 2 and 3Between lily pads 2 and 4Between lily pads 3 and 4nousluqoq6/5 feet2 feet3/2 feet6/7 feet1/2 feet3/4 feetinco20199 13.A hospital is interested in tracking the movements ofheart patients through different units. The four units of interestare emergency admissions, surgery, intensive care, and recov-ery. Emergency patients (that is, people who have suffered heartadmissions) are always assigned to the intensive care unit for aattacks and were brought into the hospital through emergencyperiod of observation following the emergency treatment. Oncea doctor determines that it is safe to do so, the patient is moved toa recovery unit. Of course, a relapse requires a return tointensive care. The surgical unit receives patients of two kinds:those who are scheduled for heart operations through non-emergency procedures (planned operations), and those whocome from intensive care (semi-emergency operations). Onlyone patient in a hundred dies in surgery; the rest are alwaysmoved to intensive care after surgery. Of the patients in inten-sive care, whether or not they have previously had surgery,about 10 percent will undergo surgery; the others are moved intorecovery after some period of intensive care. Once into recov-ery, most patients (95 percent) eventually either recover suffi-ciently to be discharged, but about 2 percent have to be returnedto intensive care. The others die in recovery. Draw a transitiondiagram, and set up an appropriate transition matrix.heFarare made.ads to be

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Answered: 9. A naturalist is observing the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

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Over the span of a month, a school tracks student choices at lunch. They find that 56% of all students buy milk with lunch and 32% buy a piece of fruit. If 22% of all students buy both milk and fruit, which of the following represents the percent of students who buy neither? (1) 28% (3) 42% (2) 34% (4) 46%
When looking at the data for graduate school admissions between men and women, it is shown that about 45% of men are admitted but only 38% of women. However, when the data is broken down by school it turns out that, within each school, the women are admitted at higher rates than the men. This could happen because I. The women apply in higher numbers to schools with lower acceptance rates. II. The women apply in higher numbers to schools with higher acceptance rates III. The men apply in higher numbers to schools with lower acceptance rates IV. The men apply in higher numbers to schools with higher acceptance rates
ta If Jane can finish the job in 6 hours while Jenny can finish the same job in 9 hours, how would you represent the time it takes them to finish the job if they work together?
H3.
In a computer game, different units are created randomly with different levels of range and Aggression according to the table below. Range is how far the unit can attack without moving, and Aggression is used to determine how far a unit will move to attack without direct command. Range Total 1 2 4 5 0.2 0.15 0 0.35 Aggression 3 0.1 0.15 0.1 0.35 0 0 0.05 0.25 0.3 Total 0.3 0.35 0.35 1 Calculate the Expected value of aggression for the units created. (E(Aggression))
116. For a device to work properly, three subsystems of the device must all function properly. To increase the reliability of the device, spare units may be added to each system. It costs 100 TL to add a spare unit to system 1, 300 TL to system 2, and 200 TL to system 3. As a function of the number of added spares (a maximum of two spares may be added to each system), the probability that each system will work is given in Table. Use dynamic programming to maximize the probability that the device will work properly, given that 600 TL is available for spare units. Identify and explain decision variables, stages, states and formulate a recursion to design the device with optimal reliability. Probability that a system works system 1 Number of spares system 3 system 2 .60 .85 .70 1 .90 .85 .90 2 .95 .95 .98 117. You are planning on moving to a new house. You need to move n items of size aj , j-1,2,.,.n. You have bought m boxes (box i has size bi , i- 1,2,.,m). You need to rent a truck that…
edo exercises 17 and 18 in section 8.1 of your textbook, about the small animal who lives in an area with woods and meadows, using the following data:If the animal is in the woods on one observation, then it is twice as likely to be in the woods as the meadows on the next observation. If the animal is in the meadows on one observation, then it is three times as likely to be in the meadows as the woods on the next observation.Assume that state 1 is being in the meadows and that state 2 is being in the woods.(1) Find the transition matrix for this Markov process. (2) If the animal is initially in the woods, what is the probability that it is in the woods on the next three observations? (3) If the animal is initially in the woods, what is the probability that it is in the meadow on the next three observations?
QUESTION 20 Polly is a driving test examiner and has kept records of all the tests she has conducted over the last year. Overall 60% of her candidates passed. Her data is shown in the table below. % who had more than 20 lessons 30 % who both had more than 20 lessons and passed the test 25 % who took the test on a Monday 20 % who both took the test on a Monday and passed the test 12 % who were aged over 25 10 % who both took were aged over 25 and passed the test 6 % who wore glasses 55 % who both wore glasses and passed the test 33 Which ONE of the following pairs of probabilities does Polly’s data suggest are NOT independent probabilities? A. Having more than 20 lessons and passing the test. B. Taking the test on a Monday and passing the test. C. Being aged over 25 and passing the test. D. Wearing glasses and passing the test.
You randomly recruit 23 students and tell each of them to come to the lab in two different mornings: each morning they will be offered some breakfast and will take a test. Each student will receive the light breakfast one time and the nutritious breakfast the other time (some will receive the light breakfast first, the others will receive the nutritious breakfast first, and the second time they switch). The average difference in a student’s score after eating the nutritious breakfast and their score after eating a light breakfast is 4.5, and the standard deviation of this difference is 3.6. (a) Construct a 95% confidence interval for the difference in the average score of students after having a nutritious breakfast and the average score of students after having a light breakfast.
a. Find the probability that the device A functions but the device B does not. b. Find the probability that the device A or the device B or both function. c. Find the probability that the circuit operates. d. It is known that the circuit is operating, find the probability that device A is functional.
3. The point guard of a basketball team has to make a decision about whether or not to shoot a three- point attempt or pass the ball to another player who will shoot a two-point shot. The point guard makes three-point shots 30 percent of the time, while his teammate makes the two-point shot 48 percent of the time. X; 3 0 P(x;) 0.30 0.70 X; 2 0 P(x;) 0.48 0.52 a. What is the expected value for each choice? b. Should he pass the ball or take the shot himself? Explain.

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