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Unformatted text preview: — £55.5sz COPY " Date: November 28, 2008
Time: 18:0020:00
Instructor: Dilek Gﬁvenc ,/ . ,/ IMPORTANT 1 Check that there are i question in your oklet I 2 Do NOT use your mobile phone a c culat ' . Turn it off during the exam. 3 Show all your work. Correct result thou sufﬁcient explanation and correct notation might
not get full credit. i I 4 Write your name on each page. ! GOOD LUCK! uuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuuu 1. Assume that the probability of errorfree transmission of a message over a
communication channel is 0.95. If a message is not transmitted correctly, a
retransmission is initiated. This procedure is repeated until a correct transmission
occurs. Assuming that successive transmissions are independent, What is the
probability that exactly eight retransmissions are required to have the third correct
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N 0 {/ISX/0f9> 0%....— NAME: .......................... 2. A system with three independent components works correctly if at least one
functions properly. Failure times of components are exponential with means of
10 000, 20 000 and 40 000 hours, respectively. Determine the probability that system will work for 1000 hours. X2"/0~1W4 94m; elf Hm. Zma/ mnjfwmil— X7. ' / 2.0 000
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1. ——i~ *1 : /__ (0,095)(a,04§)(0,025): 5,9?38 N I a) NAME: .......................... 3. Suppose that demand on a given product, during a given day X, has a Poisson
distribution so that P(X = O) = P(X =1) .
a) If a merchant stocks 2 units of the product, what is the probability that
demand will exceed the supply?
b) How many units should the merchant stock if he wishes the probability that demand will exceed the supply to be at most 0.01?
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which is unifonnly distributed over the interval 10:30 to 10:45. What is the
probability that _ a ) a) she will arrive to the classroom at least 2 minutes early. ( 5 F ‘7' H b) If there are 36 students in tln's class and the arrival time of each
student independently uniform over the interval 10:30 to 10:45,
approximate the probability that more than half of them arrives at least
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two times a month on the average. a) Find the probability that occurrence of the second emission will take
at least 40 days. (75' W9”? ['5 J
b) Suppose that waiting time between two consecutive emissions has Weibull distribution with parameters or = 0.01 and B =2. Find the .
expected time between two consecutive emissions. ( 5 fag/941(3) ,}\£:H:Z 5:11 ”2.04%: 30 0/44ng . _ 2 _._/__
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