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Unformatted text preview: MA206 Suggested Problems
Lesson '10: Exponential Distribution Let X E the time between crashes in days of the corps of cadets network server. The cumulative
distribution function oins as follows: l~— 602“ x _>_ O
F x =
( ) i0 x < 0 a. Take the derivative ofF(x) to ﬁnd the PDF of X ; ensure that you completely specify the
PDF using the appropriate intervals. / C) :1 we‘th {
as eg x > ) K C
C? , ix” (3 b. Sketch the PDF and the CDF of X. Comment on the relationship between the PDF and the CDF. ,
PM” stare at” (am) “Ni Citﬂrﬁwfis mwammimiiyw iS‘iu‘rh (Catt; {gwg
(’ipfg’ﬁiwiﬁéU it»? ‘7 ’55 i b 0. Calculate the average time between crashes. 0‘?" ,4,
E310 ,«(xtZ" g wits») dis» “(5’ $75 {r WW0 d. Compute the variance of the time between crashes. «2745 X we: to
wet} L e. Using both the PDF and the CDF, ﬁnd the probability that there are between 5 and 10
days before the next crash. Illustrate your answers on the respective graphs. CE)? f. Determine the median time between crashes. at)?“ greet» >2 22a ) g. Find the 90‘11 percentile of the random variable X. an: my W a . Mm h. Given that the cadet network has not crashed for the past 6 days, what is the probability
that the network will work for at least 3 more days before crashing? , r (
ﬂqtvwef'y i655 {Du/726ml. 7, g, ...
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This note was uploaded on 04/07/2010 for the course MA & ME 206 & 387 taught by Professor N/a during the Spring '10 term at West Point.
 Spring '10
 N/A

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