20082ee131A_1_HW5

20082ee131A_1_HW5 - EE 131A Homework #5 Due May 7th Read...

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EE 131A Homework #5 Spring 2008 Due May 7th K. Yao Read Leon-Garcia (3rd edition), pp. 148-180. 1. If the probability of hitting a target is 0.2 and ten shots are fired independently, what is the probability that the target will be hit at least once? At least twice? 2. Consider the close relationship between exponential waiting time and Poisson num- ber of arrivals. Assume the arrivals are independent. Let λ be the arrival rate (i.e., average number of arrivals per unit time). Let X be the waiting time for the next arrival (i.e., the waiting time between arrivals.) Assume the average number of arrivals in x unit time, denoted by λx, be Poissonly distributed. Denote F X ( x ) to be the cdf of X. Clearly, X 0 , since the waiting time can not be negative. Thus, F X ( x ) = 0 for x 0 . For 0 x, F X ( x ) = P ( X x ) = 1 - P ( X > x ) . But P ( X > x ) = P (noarrivalsin x unittime) . But λx is Poissonly distributed. Thus, P (noarrivalin xunit time) = exp( - λ x)( λ x) 0 / (0!) = exp(
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20082ee131A_1_HW5 - EE 131A Homework #5 Due May 7th Read...

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