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# homework5 - (c Find the expected number of ﬁsh that he...

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Stochastic Processes nctuee07f Homework 5 Due on Monday, 01/07/2008 , 1:00 pm at EC 713 1. Suppose the number of fish that a fisherman catches follows a Poisson process with rate λ = 0 . 5 per hour. The fisherman will keep fishing for two hours. If he has caught at least one fish, he quits. Otherwise, he continues until he catches at least one fish. (a) Find the probability that he stays for more than two hours. (b) Find the probability that he catches at least three fish.
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Unformatted text preview: (c) Find the expected number of ﬁsh that he catches. (d) Find the expected total ﬁshing time, given that he has been ﬁshing for four hours. 2. Problem 8.29 in textbook. 3. Follow the notations in the lecture note for this problem. Justify that the innovations process is white, and give an expression for the correlation matrix E [˜ z [ i +1 | i ]˜ z H [ j +1 | j ]] for all i and j . 4. Problem 9.10 in textbook....
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