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Exp Dist BP Soln - SCDLWL/CE’MZIZGN MA206 Probability&...

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Unformatted text preview: SCDLWL/CE’MZIZGN MA206 - Probability & Statistics Lessons 10 & 11: Probability Theory and Software Development I & II 1. The survival time in days of a soldier exposed to a chemically contaminated environment follows an exponential distribution with parameter 1 =0.053. -a. What is the probability that the soldier survives for more than 21 days? fix :2: 21) z (13sz b. What is the probability that the soldier survives between 15 and 18 days? 906%: X :2 1‘3)?“ QOWL; c. What is the probability that the soldier survives less than 1 day? RX :2: 1): drama 2. The time in days between breakdowns of the USCC e-mail server is exponentially distributed with A = 0.216. a. What is the expected time between server breakdowns? ‘ 3 Alba? days b. What is the median time between server breakdowns? 50”" Pena/7%,; [e 3‘, 2/ days 0. What is the probability that the server will break down within 5 days of its last failure? F(>< M); Mém/ d. What is the probability that after the server is repaired it lasts at least a week before failing again? [TX :37): o. 2: 205' e. If the server has performed satisfactorily for six days, what is the probability that it lasts at least two additional days before breaking down? 1 Men/wrfl/figg ftvkflpekv 2 Z): O’ 3. The time between arrivals of soldiers in hours at a battalion aid station is exponentially distributed with 9» = 0.864. Let A = the time between two successive arrivals. a. What is the expected time between two arrivals at the aid station? (£364): 2. M0 hrs b. What is the standard deviation of the time between arrivals at the aid station? 5A“; “V has” 0. What is the probability that the time between two arrivals is at most 75 minutes? PM =44? 75/620) = PM rm}; OMDOL, d. What is the probability that the time between arrivals at the aid station is within one standard deviation of the mean time between arrivals? WW “5% 24 {mi 4" 530 : Wm ——/./t :M 3: Mt Ha) /\_ .2, l} O a A 2. CD. at? 5'3 7 4. A first class cadet bought himself a used sports car to quickly transport him between his rockbound highland home and his numerous weekend excursion points. Unfortunately, it tended to break down quite frequently. The time between breakdowns (represented by the random variable T) can be modeled by an exponential distribution where its expected value E (T) is 16 hours' E'Crbwc—rfr 3‘0 Aafiaonwar a. ’What is the probability that the next breakdown will occur within 4 hours of the last breakdown? @(Tévalp): o, 2212 b. What is the 87th percentile of the time between breakdowns? lift”) 0.37 if}. 32,04 I/zrs ...
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