# hw6 - N with rate 1 3 per minute Assume that the bus has...

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Statistics 120A Assignment 6 Due Thursday, December 6, in class. Reading Chapter 5, particularly Sections 2, 3, 4, 5 and 9 Exercises 5.2.3, 5.2.4, 5.3.6, 5.3.7, 5.5.2, 5.4.1, 5.4.2, and the following problems. (A) A store promises to give a small gift to every thirteenth customer to arrive. If arrivals of customers form a Poisson process with rate 20 per hour, ﬁnd the probability density function of the time of arrival of ﬁrst lucky customer. (B) Arrivals of passengers at a bus stop form a Poisson process
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Unformatted text preview: N with rate 1 3 per minute. Assume that the bus has left at time t = 0, leaving no customers behind. Let T denote the time in minutes of arrival for the next bus; then the number of passengers present when it arrives will be N T . Suppose that T is independent of N (the arrival process) with uniform distribution over the interval (0 , 120]. (1) Compute IE ( N T | T ) and IE ( N 2 T | T ). (2) Compute IEN T and Var( N T ). 1...
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