IND ENG 161 Midterm: ieor161-sp2004-mt2-Lim-soln
8 Jan 2019
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1. (a) let tj denote the amount of time when exactly j components are working. , xj)) where {xj} are independent ex- ponential with rate . ) E[pro t] = e[10(t4 + t3) + 5t2 + 2t1] = 10 1. 2 (b) let li denote the lifetime of component i, then. Now let sb n denote the time of the nth arrival of process {nb(t), t 0}. Sb n is the sum of n independent exponential random variables, each of which has mean. 1/( e 1 n is gamma(n, e 1 y)) and hence: (i. e. sb. Since the cost is c per day, the total cost until we sell all 100 houses is c sb expected total pro t is therefore: the. E[revenue] e[cost] = e[100y] e[c sb. 1 (d) taking the rst derivative of (1) with respect to y and setting it equal to 0 gives. Note that the second derivative of (1) with respect to y is.
