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Unformatted text preview: kets with probability 1/10. Let Ni be the number of customers that buy i tickets in the ﬁrst hour. Find the joint distribution of (N1 , N2 , N3 ). 2.44. Ellen catches ﬁsh at times of a Poisson process with rate 2 per hour. 40% of the ﬁsh are salmon, while 60% of the ﬁsh are trout. What is the probability she will catch exactly 1 salmon and 2 trout if she ﬁshes for 2.5 hours? 2.45. Signals are transmitted according to a Poisson process with rate . Each signal is successfully transmitted with probability p and lost with probability 1 p. The fates of di↵erent signals are independent. For t 0 let N1 (t) be the number of signals successfully transmitted and let N2 (t) be the number that are lost up to time t. (a) Find the distribution of (N1 (t), N2 (t)). (b) What is the distribution of L = the number of signals lost before the ﬁrst one is successfully transmitted? 2.46. A policewoman on the evening shift writes a Poisson mean 6 number of tickets per hour. 2/3’s of these are for speeding and cost \$100. 1/3’s of these are for DWI and cost \$...
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This document was uploaded on 03/06/2014 for the course MATH 4740 at Cornell University (Engineering School).

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