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Unformatted text preview: busy periods with more than one customer will be high. P a r t (d) Let a state with a prime (1',2',3' ...) indicates a state in which the first customer after an idle period is still receiving service. States 1,2,3 ... are states in which the first customer after an idle period has already left the system. Problem 3 Part (a) Suppose we have cdf Fx(x) and pdf f,(x) and we are told that Y = a x , where a > 0. Here Y = 200X1 i.e., a = 200. That is, we have scaled all distances from 1to 200. Thus, So, before truncation, we have 1 1 fy (Y) = ZGr 1 + (y/200)2 for all values of y. Truncation event = T = 200 < Y < 200. So, we can finally write, 1 fylT(~lT) = ~ Y ( Y ) / ~ T ( ~ ) = (l/loh) for 200 < y < 200 1 + ( ~ / 2 0 0 ) ~ Part (b) Mean = 0 by symmetry and finiteness of the pdf. Variance is finite by bounded pdf. Part (c) Question asks for...
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This note was uploaded on 11/08/2011 for the course AERO 16.72 taught by Professor Hansman during the Fall '06 term at MIT.
 Fall '06
 hansman

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