E270 CH3 outline

E270 CH3 outline - Discrete versus constinuous random...

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Discrete versus constinuous random variables Discrete random variable x 0 0.2373 1 0.3955 2 0.2637 3 0.0879 4 0.0146 5 0.0010 1.0000 Probability Density Function Continuous random variable The Normal Distribution µ = 10 µ = 10 σ = 4 σ = 10 Finding Probabilities in a Normal Distribution Example Assume the vehicle speed on a freeway is normal y distributed with μ = 78 mph σ = 8 mph If a vehicle is clocked at random, what is the probability that the speed is at or below 70 mph? What proportion or percentage of vehicles drive at or below 70 mph? x = 70 P(x ≤ 70) z P(Z < z) -1.00 0.1587 σ = 8 z = (70 − 78) ∕ 8 = -1.00 P(z < -1.00) = 0.1587 What is the probability that the speed is above 90 mph? What proportion or percentage of vehicles drive above 90 mph? μ = 78 x = 90 P(x > 90) σ = 8 z P(Z < z z P(Z < z) -1.50 0.0668 1.50 0.9332 z = (90 − 78) ∕ 8 = 1.50 P(z > 1.5) = 1 - P(z < 1.5) = 0.0668 OR: P(z > 1.50) = P(z < -1.50) = 0.0668 What is the probability that the vehicle speed is between 66 and 90 mph? What proportion or percentage of vehicles drive between 66 and 90 mph? μ = 78 66 σ = 8 90 P(66 < x < 90) z P(Z < z z P(Z < z) -1.50 0.0668 1.50 0.9332 (66 - 78) / 8 = -1.5 (90 - 78) / 8 = 1.5 P(-1.50 < z < 1.50) P(z < 1.50) = 0.9332 P(z < -1.50) = 0.0668 0.8664 What is the probability that the vehicle speed is within ±10 mph from the mean? What proportion or percentage of vehicles drive within ±10 mph from the mean? 10

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This document was uploaded on 10/27/2011 for the course ECON-E 270 at Indiana.

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E270 CH3 outline - Discrete versus constinuous random...

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