Q2. Consider a company that is going to build a new manufacturing system and would liketo determine the long-run (steady-state) mean hourly throughput of their system after it hasbeen running long enough for workers to know their jobs and for mechanical difficultiesto have been worked out. The system will operate continuously 24 hours a day for 7 daysa week. Let N; be the number of parts manufactured in the ih hour. If the stochastic processN1, N2, .. has a steady-state distribution with corresponding random variable N, then weare interested in estimating the steady-state mean v = E(N).

The system operates continuously 24 hours a day 7 days a week.The number of parts manufactured in…

Answered: to know their jobs and for mecha

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 Xn is an IID Gaussian process, withµX[n]=1, and σ2 X[n]=1Now, another stochastic process Yn = Xn − Xn−1. Please find:(a) The mean µY (n).(b) The variance σ2Y (n).(c) The auto-correlation RY (n, k)
A cellphone provider classifies its customers as low users (less than 400 minutes per month) or high users (400 or more minutes per month). Studies have shown that 80% of people who were low users one month will be low users the next month, and that 70% of the people who were high users one month will high users next month. a. Set up a 2x2 stochastic matrix with columns and rows labeled L and H that displays these transitions b. Suppose that during the month of January, 50% of the customers are low users. What percent of customers will be low users in February? In March?
Consider a simple model of the hunting behaviour of a fox. In a single day, the fox catches either 0 or 1 rabbits, with probabilities 0.3 and 0.7, respectively. The outcome of hunting on day m is independent of all other days.We describe this system through a discrete-time, discrete-state stochastic process R(m), where R is the total number of rabbits caught between the end of day 0 (deﬁning a starting point of our observation) and the end of day m. m = 0,1,2,3... is thus a discrete time parameter, and R(0) = 0 by deﬁnition (a) It can be shown that pr(m) – the probability of catching R = r rabbits in m days – is given by a binomial distribution (see Appendix A.2.1). Here, m is the number of “trials”, r the number of successes and q = 0.7 the probability of success. Hence give expressions for:i The mean number of rabbits caught after m days. ii The standard deviation of the total number rabbits caught after m days. iii The standard deviation of the mean number of rabbits caught per day…
When would simulation NOT be a good choice for studying a system? A. When the system is too complex B. When the input variables do not conform to probability distributions prescribed in the mathematical models C. When an optimal solution is needed D. When the mathematical models are too difficult to solve
"NEED HELP ASAP" For a certain group of states, it was observed that 60% of the Democratic governors were succeeded by Democrats and 40% by Republicans. Also, 20% of the Republican governors were succeeded by Democrats and 80% by Republicans. (a) Set up the 2×2 stochastic matrix with columns and rows labeled D and R that displays these transitions. (b) Compute A2 and A3. (c) Suppose that all the current governors are Democrats. Assuming that the current trend holds for three elections, what percent of the governors will then be Democrats? D R (a) The stochastic matrix is D nothing nothing R nothing nothing (b) A2= A3= (c) nothing% of the governors will be Democrats after three elections.
27. An article in Radio Engineering and Electronic Physics (1980, Vol. 25, pp. 74-79) investigated the behavior of a stochastic generator in the presence of external noise. The number of periods was measured in a sample of 100 trains for each of two different levels of noise voltage, 100 and 150 mV. For 100 mV, the mean number of periods in a train was 7.9 with s1 = 2.6. For 150 mV, the mean was 6.9 with s2 = 2.4. Use α = 0.01 and assume that each population is normally distributed and the two population variances are equal. (a) It was originally suspected that raising noise voltage would reduce mean number of periods. Do the data support this claim? (b) Calculate a confidence interval to answer the question in part (a).
why is the covariance of a deterministic and a stochastic process 0? This relats to Arithmetic Bronian Motion
Given three independent Bernoulli processes Xn, Yn, Zn with success probabilities given as 0.10, 0.87, and 0.26, respectively. X and Y are merged into one Bernoulli process which is merged with Z after. Find the resulting success probability of the last Bernoulli process. (Note: the answer should be in 4 decimal points)
Suppose two forces Red and Blue, with Red having a starting force = 2, and Blue having a starting force = 1. Engage in a stochastic Lanchester battle assuming square law, in a fight-to-the-finish, with Red a = 0.01 casualties per minute, and Blue b = 0.03 casualties per minute. (a) What is the expected time of the first casualty?(b) What is the probability that there are no casualties in the first 20 minutes?(c) What is the expected number of Red survivors and the expected length of the battle?
Consider the following stochastic system. Let Xn be the price of a certain stock (rounded to the nearest cent) at the time that the stock market closes on the n-th day starting today. Would it be appropriate to model this system as a Discrete-time Markov Chain?
Refer to Exercise 12 in Section 3.2. Assume that τ0 = 50 ± 1 MPa, w = 1.2 ± 0.1 mm, and k= 0.29 ± 0.05 mm−1.a) Estimate τ, and find the uncertainty in the estimate.b) Which would provide the greatest reduction in the uncertainty in τ: reducing the uncertainty in τ0 to 0.1 MPa, reducing the uncertainty in w to 0.01 mm, or reducing the uncertainty in k to 0.025 mm−1?c) A new, somewhat more expensive process would allow both τ0 and w to be measured with negligible uncertainty. Is it worthwhile to implement the process? Explain.
In the B&K model of Example 18.5-1, suppose that the interarrival time at the checkout area is exponential with mean 5 minutes and that the checkout time per customer is also exponential with mean 10 minutes. Suppose further that will add a fourth counter. Counters 1,2, and 3 will open based on increments of two customers and counter 4 will open when there are 7 or more in the store. (a) The steady-state probabilities, for all . (b) The probability that a fourth counter will be needed. (c) The average number of idle counters.

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