6.262 Discrete Stochastic Processes, 2011 Final Exam Solutions
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چکیده
a) Let Z be the time at which the last student finishes. Show that Z has a distribution function FZ (z) given by [1 exp( z] . b) Let T1 be the time at which the first student leaves. Show that the probability density of T1 is given by n e n t . For each i, 2 i n, let Ti be the interval from the departure of the i 1st student to that of the ith. Show that the density of each Ti is exponential and find the parameter of that exponential density. Explain why each Ti is independent. Finally note that Z = Pn Ti. i=1
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