00095 x 00545 x 45 0 a mall is planning for snow

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Unformatted text preview: rm is 1 = (Σ x2 P(x))  ­ 2µ2 + µ2 = (Σ x2 P(x))  ­ µ2 QED 3) A European train arrives at a station every 30 minutes. American tourists have not checked the schedule and each person’s waiting time is a random variable with a continuous uniform distribution. Let’s get the distribution first 4/7 CEE 202 – Engineering Risk & Uncertainty Spring 2011 (Bond) Homework 5 Expected Values, More Distributions a) What is the probability that a tourist waits more than 20 minutes? The tourist won’t wait more than 30 minutes (because the pdf is 0 after that point), so we want P(20≤X≤30). Both of these values are within the range 0 ­30. d − c 30 − 20 =0.333 P (c ≤ X ≤ d ) = = B − A 30 − 0 b) What is the probability that two tourists not traveling together each wait between 4 and 10 minutes? 10 − 4 P ( 4 ≤ X ≤ 10) = = 0.2 30 =0.333 If two tourists are not traveling together, it means that they are statistically independent, the probability that two tourists each wait between 4 and 10 minutes is € € 4) In snowier Chicago, the probability density function of annual snowfall, in inches, is # x < 10 0, % 10 " x < 45 f ( x ) = $ "0.00095 x + 0.0545, % x # 45 0, & A mall is planning for snow removal. They expect to spend $400 per inch plus a flat fee of $1000 per year. a) What are the expected value and standard deviation of annual !...
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