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# Lesson 10 - MA206 Suggested Problems Lesson'10 Exponential...

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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‘r-h (Catt; {gwg (’ipfg’ﬁiwiﬁéU it»? ‘7 ’55 i b 0. Calculate the average time between crashes. 0‘?" ,4, E310 ,«(xt-Z" 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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Lesson 10 - MA206 Suggested Problems Lesson'10 Exponential...

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