TP%2314_f08 - CE 3102 Fall 2008 Thought Problem 14...

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CE 3102 Fall 2008 Thought Problem 14 Functions of Random Variables 300 200 100 0 15 10 5 0 headway Frequency The graph above shows a frequency distribution for vehicle headways on Irving Ave., between Lincoln and Franklin, in Minneapolis. (a) Identify an appropriate probability model for these data. (b) What is the probability of headway (gap) less than 100 seconds? Less than 10 seconds?
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CE 3102 Fall 2008 Thought Problem 14 Instructor’s Partial Solution Let Y denote the time between successive vehicle arrivals (headways.) When observed data tend to show (a) restriction to non-negative values (b) definite positive skew (c) a definite non-zero mode One way to get a random variable with this sort of behavior is to exponentiate a normal random variable. That is, if X is a normal random variables with mean X μ and variance 2 X σ Y=exp(X). For some reason, a random variable that is the exponential of a normal random variables is called a lognorma l random variable. The exponential function is strictly monotonic, so
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TP%2314_f08 - CE 3102 Fall 2008 Thought Problem 14...

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