A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The transition matrix representing the transition probabilities from one state to another is Elec. Gas Oil Solar Electricity .70 .15 .90 .20 .05 Natural Gas .05 .02 .75 Fuel Oil .10 .08 .05 .95 Solar Energy Among homeowners within the area, 25% currently use electricity, 40% use natural gas, 30% use oil, and 5% use solar energy as the major source of heat for their homes. What is the expected distribution of the homeowners that will be using each type of heating fuel or solar energy within the next decade? (Round your answers to two decimal places.) electricity X % natural gas % fuel oil X % Enter a number. solar energy

A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The transition matrix representing the transition probabilities from one state to another is Elec. Gas Oil Solar Electricity .70 .15 .90 .20 .05 Natural Gas .05 .02 .75 Fuel Oil .10 .08 .05 .95 Solar Energy Among homeowners within the area, 25% currently use electricity, 40% use natural gas, 30% use oil, and 5% use solar energy as the major source of heat for their homes. What is the expected distribution of the homeowners that will be using each type of heating fuel or solar energy within the next decade? (Round your answers to two decimal places.) electricity X % natural gas % fuel oil X % Enter a number. solar energy

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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5. Given the following state transition graph and emission probabilities for each state a State 1 Output Prob 0.8 b 1 C 0.5 0.1 0.1 0.3 2 a State 2 Output C 0.5 0.2 Prob 0.2 0.6 0.2 0.5 3 State 3 Output 1 C Prob 0.7 a b 0.2 0.1 What's the probability of observing "aabbc" through state transition path 1-2-2-3-3?||
A city uses three pumps to carry water from a river to a reservoir. Pumps A and B are new, and have a probability of failing of 0.015 on any day. Pump C is older, and has a probability of failure of 0.08 on any day. Pumps A and B operate Monday-Friday. On Saturday, pumps A and C operate while pump B is serviced. On Sunday, pumps B and C operate while pump A is serviced. Answer the following questions, assuming that the pumps operate independently of one another, and independently from day to day. Determine the probability that pump A works on a day that it is in use. Find the probability that pumps A and B both fail on a day they are both in use. Compute the probability that at least one pump fails on any Sunday. Find the probability that pump A works, and C fails on any Saturday. Determine the probability that no pumps fail in a week.
The four brands of soap have the current market share of 0.23, 0.28, 0.25, and 0.24 for brands A, B, C, and D, respectively. Below are the transition probability matrix of the soap brands based on their annual performance and the number of customers using the brands. 0.4 2300 T 0.3 2800 0.2 2500 2400 From/To A B C D A 0.2 0 0.3 0.3 B 0.3 0.2 0.5 0.4 C 0.1 0.5 0 0.3 D 0 a) What is the market share of Brand D in the long run? Answer in 2 decimal places. c) What is the mean return time of Brand A? Answer in 2 decimal places. b) How many customers will shift preference in using Brand C soap in the long run? Number of Customers d) What is the percentage change of Brand B? Answer in percentage and in 2 decimal places.
Consider an M/M/1 queueing system. Find the probability of finding at least n customers in the system.
Many investors and financial analysts believe the Dow Jones Industrial Average (DJIA) gives a good barometer of the overall stock market. On January 31, 2006, 9 of the 30 stocks making up the DJIA increased in price (The Wall Street Journal, February 1, 2006). On the basis of this fact, a financial analyst claims we can assume that 30% of the stocks traded on the New York Stock Exchange (NYSE) went up the same day.A sample of 80 stocks traded on the NYSE that day showed that 11 went up.You are conducting a study to see if the proportion of stocks that went up is is significantly less than 0.3. You use a significance level of α=0.02α=0.02.What is the test statistic for this sample? (Report answer accurate to three decimal places.)test statistic = What is the p-value for this sample? (Report answer accurate to four decimal places.)p-value = The p-value is... less than (or equal to) αα greater than αα This test statistic leads to a decision to... reject the null accept the null fail…
The purchase patterns for two brands of toothpaste can be expressed as aMarkov process with the following transition probabilities: Which brand appears to have the most loyal customers? Explain.
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A study conducted by the Urban Energy Commission in a large metropolitan area indicates the probabilities that homeowners within the area will use certain heating fuels or solar energy during the next 10 years as the major source of heat for their homes. The following transition matrix represents the transition probabilities from one state to another. Electricity 10.2 Natural Gas Fuel Oil Solar Energy Elec. Gas Oil 0.60 0.05 0.10 0.15 0.85 0.10 0.08 Solar 0 0.10 0.02 0.75 0.08 0.15 0.08 0.05 0.84 Among homeowners within the area, 20% currently use electricity, 35% use natural gas, 40% use oil, and 5% use solar energy as the major source of heat for their homes. In the long run, percentage of homeowners within the area will be using solar energy as their major source of heating fuel? (Round your answer to one decimal place. Assume the trend continues.) X % what
Is there a unique way of filling in the missing probabilities in the transition diagram shown to the right? If so, complete the transition diagram and write the corresponding transition matrix. If not, explain why. O A. A P = B A A B C 0.5 0.3 0.6 0.4 B 0.2 Is there a unique way of filling in the missing probabilities in the transition diagram? If so, identify the missing probabilities. If not, explain why. Select the correct choice below and, if necessary, fill in the answer boxes to complete your choice. ⒸA. Yes. The probability of transition from A to A is 0.2, the probability of transition from B to C is 0.2, and the probability of transition from C to B is 4. (Type integers or decimals.) O B. No. It is possible to find the probability of transition from B to C and from C to B, but there is not enough information to find the probability of transition from A to A. O C. No. At least one of the missing probabilities is needed to find the other two. O D. No. It is possible to find the…