tut12 - The system will fail if either of the two...

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Page 1 of 2 COMP211 Data and System Modeling (PROB/STAT) Tutorial (Week 12) 1. A person arrives at a certain bus stop each morning. The waiting time, in minutes, for a bus to arrive is uniformly distributed on the interval (0, 15). (a) Find the mean waiting time. (b) Find the standard deviation of the waiting times. (c) Find the probability that the waiting time is between 5 and 11 minutes. (d) Suppose the waiting times on different mornings are independent. What is the probability that the waiting time is less than 5 minutes on exactly 4 of 10 mornings? 2. Let T (4, 0.5) (a) Find μ T . (b) Find T . (c) Find P( T ≤ 1) (d) Find P( T ≥ 4)
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Page 2 of 2 3. A system consists of two components connected in series.
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Unformatted text preview: The system will fail if either of the two components fails. Let T be the time at which the system fails Let X 1 and X 2 be the lifetimes of the two components. Assume that X 1 and X 2 are independent and that each has the Weibull distribution with α = 2 and β = 0.2. (a) Find P( X 1 > 5). (b) Find P( X 1 > 5 and X 2 > 5). (c) Explain why the event T > 5 is the same as the event { X 1 > 5 and X 2 > 5}. (d) Find P( T ≤ 5). (e) Let t be any positive number. Find P( T ≤ t ), which is the cumulative distribution function of T . (f) Does T have a Weibull distribution? If so, what are its parameters. 4. Let X  Geom( p ). Find the Maximum Likelihood Estimator (MLE) of p ....
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