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Unformatted text preview: Page 1 of 3 COMP211 Data and System Modeling (PROB/STAT) Tutorial (Week 8) -Answer 1) In the past year there were 30 days on which accidents occurred along a certain stretch of highway. Assume that the probability that an accident occurs on any one day is 30/365 and that each day is independent of the others. What is the probability that there will be no accidents during the first 2 weeks of January? What is the probability that the first accident occurs on 3 rd day? Solution: Label the result “accident on j th day” as “success at j th trial.” Thus each day corresponds to one Bernoulli trial. The waiting time until an accident is therefore geometrically distributed with p = 30/365; thus P(no accident during first 2 weeks of January) = P ( W > 14) = g1 − G¡ G¢£ ¤ ¥¦ = 0.3010 P(the first accident occurs on 3 rd day) = P( W = 3 ) = g1 − G¡ G¢£ ¤ § ( G¡ G¢£ ) = 0.0692 2) Let Y be the number of successes in n independent repetitions of a random experiment having the...
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This note was uploaded on 04/08/2012 for the course COMP 211 taught by Professor Dr.kwok during the Spring '12 term at Hong Kong Polytechnic University.
- Spring '12