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Unformatted text preview: Date: January 9, 2008 Time: 15:3017:30 . // Instructor: Dilek Giivenc MATH 230 F IMPORTANT
1 Check that there are 5 questi ns in y 2 Do NOT use your mob le p me as a alcu tor. T 3 Show all your work. Co cc results w t ut su cient explanation and correct notation might
not get full credit. ‘ 4 Write your name on each 1 2 4 5 TOTAL
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20 20 20 20 100 GO D LUCK & HAVE A NICE BREAK!
1. Jobs arriving to a computer server have been found to require CPU time that
can be modeled by an exponential distribution with mean 140 ms. The CPU
scheduling discipline is quantumoriented so that a job not completing within
a quantum of 100 ms will be routed back to tail of "the queue of waiting jobs.
3) Find the probability that an arriving job is forced to wait for a second
quantum. (7 points)
b) What is the probability that the third arriving job of a day will be the
ﬁrst one that is forced to wait for a second quantum? (7 points) c) Of the 800 jobs coming in during a day, how many are expected to
ﬁnish within the ﬁrst quantum? (6 points) , J, ‘ =4. #743 X> o
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b) Let X , ,X 2 ,  X100 be a random sample of random variable X whose .c.d.f given above (or p.d.f given in part (a) ). Find the probability that sample mean
of this sample will be at least 1. (12 points) ) la!) /.9/* (it/(41 /£K): Clix) 5%
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I : /, £00737: 0.9?82 NAME: .......................... 3. Let X l , X 2 ...X,; be a random sample of random variableX , Where f (x)
is gamma density with parameters a = 3 and unknown [3. a) Find the maximum likelihood estimator of [3. (8 points) b) Is the estimator in part (a) an unbiased estimator for [3? Why? (6 points)
c) Find the variance of the estimator in part (a). ( 6 points) *3: 'L ”.5.
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355' NAME: .................. 4. In a study of estimating the average response time of a web server, 16
independent eXperiments are conducted and from each average of
successive response times are calculated. The average of the results of 16
experiments was found to be 0.68 second and standard deviation was
found to be 0.05 second. a) Estimate the true mean response time of this web server with a
95% conﬁdence interval. (9 points) b) Estimate the true standard deviation of response times of this server
with a 90% conﬁdence interval. (8 points) c) State your assumption(s) for your answers in parts (a) and (b) to be
valid. (3 points) .015 ___.
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variance of 900. A reorganization of the program’s address space was
suspected to have improved its locality and hence decreased its average
workingset size. In order to judge locality—improvement procedure, 100
samples of the "‘improved” version of the program’s workingset size were
taken and sample average was found to be 45 pages. ' a) Is there enough evidence to believe that the reorganization indeed
improved program locality? Test at or =0.05. Calculate Pvalue of
the test. (10 points) b) Calculate the probability of making type 11 error in testing the
hypothesis in part (a) when uA = 47. (10 points) #:1ch )7?%5 wiawo) F230 0» awe 2,1: ”Jab/ﬂ
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