# ex_5 - U> s,V> t(b Let t → 0 and s → 0 in the...

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Spring 2009 OR3510/5510 Problem Set 5 In view of the coming Prelim, in order to smooth the TA workload, do not hand in this problem set. However, you are responsible for the material and skills represented by this problem set. Reading: We have ﬁnished Markov chains and are now in Section 5.3.4. x/y=page x, problem y in Ross. (1) A machine has two critically important parts and is subject to 3 diﬀerent types of shocks. Shocks of type i occur at times of a Poisson process with rate λ i . Shocks of types 1 break part 1, those of type 2 break part 2 while those of type 3 break both parts. Let U and V be the failure times of the two parts. (a) Find P [
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Unformatted text preview: U > s,V > t ] . (b) Let t → 0 and s → 0 in the previous part to show that U and V each have exponential distributions. (c) Are U and V independent? (2) 346/1 (3) 346/4 (4) 346/5 (5) 346/6 See page 285 for Example 5.3. (6) 347/9 (7) 351/34 (8) 352/38 (9) The data set salesdate.txt is given in course documents/data and consists of a single column with about 34000 rows. The saledate records in seconds relative to a certain initialization point dates of care sales. Note the data may not be ordered. Sort the data from smallest to biggest. Can the sorted sale dates be modelled as a Poisson process? Why or why not? 1...
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