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In Exercises 7–12, find the stable distribution for the given regular stochastic matrix.
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Finite Mathematics & Its Applications (12th Edition)
- Find the steady-state vector for A = | .7 .2 .2 | | 0 .2 .4 | | .3 .6 .4 |arrow_forwardEXAMPLE 6.67 If λ = 2 per hour and = 3 per hour in an M/M/4/N queueing system and there are 2 chairs for waiting customers, calculate the probability that there are 7 customers in the system.arrow_forwardSection II 11. Assume X is a random variable with moment generating function M(t) (0.3et +0.7), -0arrow_forward1 .2° is a regular stochastic matrix. 10. Determine if P 0.8arrow_forward(Revision.) Let X = Wo.5 + 0.5W1 – 2W2 – W3, where (W1, t > 0) is standard BM. Find the expectation E(X²).arrow_forwardEXAMPLE 6.38 Consider an M/M/c queueing system. Find the probability arriving customer is forced to join queue. that anarrow_forwardA piece of equipment will function only when the three components A, B and C are working. The probability of A failing during one year is 0.15, that of B failing is 0.05, and that of C failing is 0.10. What is the probability that the equipment will fail before the end of the year?arrow_forwardFind a steady-state vector for the stochastic matrix S = .4 .5 .8 0 .5 .1 .6 0 .1arrow_forwardThe index model has been estimated for stocks A and B with the following results: RA = 0.03 + 0.8RM + eA. RB = 0.01 + 0.9RM + eB. σM = 0.35; σ(eA) = 0.20; σ(eB) = 0.10. The covariance between the returns on stocks A and B is A) 0384. B) 0.0406. C) 0.0882. D) 0.0772. E) 0.4000. 2) Analysts may use regression analysis to estimate the index model for a stock. When doing so, the slope of the regression line is an estimate of A) the α of the asset. B) the β of the asset. C) the σ of the asset. D) the δ of the asset. Choose correct answer with justification.arrow_forwardAssume the chances of failure of each component is given in Figure. What is the probability that the system would not work? .arrow_forwardIf possible, fill in the missing values to make A a doubly stochastic matrix. (If not possible, enter IMPOSSIBLE.) - [ 0.3 a = b = A = a 0.3 X Xarrow_forwardSuppose the following expression is given: P(X5-31X4-3,X3-4,X2-1,X1-3, X0=1). Write down the "realization" of the stochastic process implied by the above expression, and explain what it means. Question 1 Imarrow_forwardarrow_back_iosSEE MORE QUESTIONSarrow_forward_ios
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