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mat2377-assignment3-no_sol

# mat2377-assignment3-no_sol - Assignment 3 Due date 11...

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Assignment 3 Due date: 11 February 2010 Total number of points: 25 Q 1. Suppose that the random variable X has the following cumulative distribution function CDF: F X ( x ) = 0 , x 0 x 3 , 0 x 1 1 , x 1 . (a) Compute P ( X > 0 . 5) and P (0 . 2 < X < 0 . 8). (b) Find the probability density function of X . (c) Find E[ X ] and Var[ X ]. Q 2. Assume that arrivals of small aircrafts at an airport can be modeled by a Poisson process with average 1 aircraft per hour. (a) What is the probability that more than 3 aircrafts arrive within an hour? (b) Consider 15 consecutive and disjoint one hour intervals. What is the probability that in none of these intervals we have more than 3 aircraft arrivals? (c) What is the probability that exactly three aircrafts arrive within 2 hours? (d) What is the length of the interval, such that probability of having no arrival within this interval equals 0.1? (e)

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mat2377-assignment3-no_sol - Assignment 3 Due date 11...

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