IND ENG 161 Midterm: ieor161-sp2007-mt2-Lim-soln
8 Jan 2019
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1. (a) let the states be the person paris has chosen to go out with, i. e. {n, b, l, s}. 1/3 1/3 1/3 (b) the transition matrix is doubly stochastic, limiting probabilities are n = b = Therefore the proportion of time paris spends with each friend is 1/4. (c) let ti, j denote the number of transitions needed to go from i to j. E[tn,s] = 1 + pn,be[tb,s] + pn,le[tl,s] = 1 + 1/3(e[tb,s] + e[tl,s]) By symmetry, e[tn,s] = e[tb,s] = e[tl,s], thus e[tn,s] = 3. 2. (a) let g be the process of green men"s arrival process, and r be the process of red men"s arrival process. min(g,r) is exponential with rate + =2+3=5. Let ti be the interarrival time between the (i-1)th arrival and ith arrival, and t be the time it takes to ll the space ship. 5 (b) for each arrival, the probability that it is a green man is.
