What is the steady-state probability vector?
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![6.
Suppose the transition matrix for a Markov process is
State A
State B
State A State B
1
1]
0
1-P р
р
9
where 0 < p < 1. So, for example, if the system is in state A at time 0 then the probability
of being in state B at time 1 is p.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1aa15229-e131-473b-bc97-7b983c6676cc%2F8b4728b3-afdd-4d82-8cdf-276cd7222bf8%2Fxix3oan_processed.png&w=3840&q=75)
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- graduate believes she has a 60% chance of getting a particular job at an Ivy League school. Historically, 75% of the candidates who got a similar job had two interviews; 45% of the unsuccessful candidates had two interviews. Apply Bayes’ Theorem to calculate the probability that this candidate will be hired, assuming she had two interviewsThe principle of redundancy is used when system reliability is improved through redundant or backup components. Assume that a student's alarm clock has a 19.1% daily failure rate. If the student has two such alarm clocks, what is the probability that they both fail on the morning of an important final exam?Two wine tasters rate each wine they taste on a scale of 1 to 5. From data on their ratings of a large number of wines, we obtain the given probabilities for both tasters' ratings of a randomly chosen wine. Taster 2 Taster 1 1 2 3 4 5 11 0.050.05 0.020.02 0.010.01 0.000.00 0.000.00 22 0.020.02 0.080.08 0.020.02 0.020.02 0.010.01 33 0.010.01 0.020.02 0.240.24 0.050.05 0.010.01 44 0.000.00 0.020.02 0.050.05 0.230.23 0.020.02 55 0.000.00 0.010.01 0.010.01 0.020.02 0.080.08 (c) What is the probability that Taster 11 rates a wine higher than Taster 2? Give your answer to two decimal places. probability:
- 20 mins leftWhich investment has the highest expected return? Which is the safest investment and why? Which is the riskiest investment and why? A. x P(x) xP(x) 7000000 0.2 1400000 0 0.3 0 -1000000 0.5 -500000 Total 900000 b. x P(x) xP(x) 3000000 0.10 3000000 2000000 0.60 1200000 -1000000 0.30 -300000 Total 1200000 c. x P(x) xP(x) 3000000 0.40 1200000 0 0.50 0 -1000000 0.10 -100000 Total 1100000Under current economic circumstances, a stockbroker estimates that a client would invest in tax-free bonds (A) with a chance of 0.6 and in mutual funds (B) with a probability of 0.3. He has a 0.15 chance of investing in both tax-free and mutual funds. Determine the probability that the consumer will not invest in any of the two options at this moment.
- In a business venture, a man can make a profit of Ksh2,000Ksh2,000 with a probability of 0.40.4 or have a loss of kshs1,000kshs1,000 with a probability of 0.6.0.6. What is his expected profit?Assume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .solve a and b fast
- You are enrolled in MBA 440. At the beginning of the semester, you used your hunch to estimate the likelihood of passing this class. Let P be the event of passing the class; F is the event of failing the class. Your prior probabilities are as follows: P(P)=0.7 P(F)=0.3 After the first week of class, you find out that you have failed the first assignment. Let A1 be the event of passing the first assignment; let A2 be the event of failing the first assignment. Now you feel you need to update your belief about the likelihood of passing this class. You talk to your Professor and she tells you that given someone has passed the class, the probability of passing the first assignment is 0.8, i.e. P(A1|P)=0.8. She also gives you the following conditional probabilities: P(A2|P)=0.2; P(A1|F)=0.3 and P(A2|F)=0.7. What is the posterior probability that you will pass this class given that you have failed the first assignment?(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?Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 30 customers per hour or 0.5 customers per minute. Let's assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 45 customers per hour, or 0.75 customers per minute. Determine the following operating characteristics for the system. (Round your answers to four decimal places.) (a) The probability that no customers are in the system 1353 (b) The average number of customers waiting 1786 (c) The average number of customers in the system 1.25 (d) The average time (in min) a customer spends waiting 4.2 X min (e) The average time (in min) a customer spends in the system x min 1 (f) The probability that arriving customers will have to wait for service 73 X
