hw22 - ENEE 324 Problem 22A ASSIGNMENT 22 Due Thu 12/10...

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ENEE 324 ASSIGNMENT 22 Due Thu 12/10 Problem 22A Consider a Poisson arrival process { N ( t ) , t > 0 } (where t is in seconds) of rate λ = 2 arrivals/sec. (i) (2 pts.) Determine P [ N (4) = 8]. (ii) (3 pts.) Determine P [ N (5) = 10 | N (1) = 2]. (iii) (3 pts.) Given that there were ten arrivals in the time interval (0 , 5], what is the conditional probability that there were no arrivals in either (0 , 1] or (4 , 5]? (iv) (2 pts.) Given that there were ten arrivals in the time interval (0 , 10], what is the conditional probability that there were no arrivals in either (0 , 2] or (8 , 10]? (v) (3 pts.) Given that there were ten arrivals in the time interval (0 , 5], what is the conditional probability that there were two arrivals every second, i.e., in (0 , 1], (1 , 2], etc.? (vi) (5 pts.) Determine P [ N (5) - N (3) = 2 | N (4) = 8]. (vii) (2 pts.) If { M ( t ) , t > 0 } is a also a Poisson arrival process with rate λ = 3 arrivals/sec, what is the relationship between the expected time of the second arrival in
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