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The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the interval that ranges from 0 km to 400 km is a reasonable model for x. (a) What is the probability that x is at most 300? (b) What is the probability that x is between 300 and 450? (c) What is the probability that x is between 150 and 300? (d) Explain why the probabilities calculated in parts (b) and (c) are equal.

The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the interval that ranges from 0 km to 400 km is a reasonable model for x. (a) What is the probability that x is at most 300? (b) What is the probability that x is between 300 and 450? (c) What is the probability that x is between 150 and 300? (d) Explain why the probabilities calculated in parts (b) and (c) are equal.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the interval that ranges from 0 km to 400 km is a reasonable model for x. (a) What is the probability that x is at most 300? (b) What is the probability that x is between 300 and 450? (c) What is the probability that x is between 150 and 300? (d) Explain why the probabilities calculated in parts (b) and (c) are equal.
Transcribed Image Text:The article "Probabilistic Risk Assessment of Infrastructure Networks Subjected to Hurricanes"t suggests a uniform distribution as a model for the actual landfall position of the eye of a hurricane. Consider the random variable x = distance of actual landfall from predicted landfall. Suppose that a uniform distribution on the interval that ranges from 0 km to 400 km is a reasonable model for x. (a) What is the probability that x is at most 300? (b) What is the probability that x is between 300 and 450? (c) What is the probability that x is between 150 and 300? (d) Explain why the probabilities calculated in parts (b) and (c) are equal.
Let x be the distance of actual landfall from the predicted landfall of the eye of a hurricane. It is given that a uniform distribution on the interval that ranges from 0 to 400 km is a reasonable model for the random variable x. The graph of a uniform probability density function is a rectangle with an area equal to 1. The base, or width, of the rectangle is the range of the random variable x. Here, x is in the interval 0 < x < 400, so the length of the rectangle's base is Substitute the area and base into the formula for the area of a rectangle to find the height. area = (base)(height) --?-- )(theight) 1 = 1 height = Of interest is the probability that x is at most 300, giving the probability statement P 2- v 300).
Transcribed Image Text:Let x be the distance of actual landfall from the predicted landfall of the eye of a hurricane. It is given that a uniform distribution on the interval that ranges from 0 to 400 km is a reasonable model for the random variable x. The graph of a uniform probability density function is a rectangle with an area equal to 1. The base, or width, of the rectangle is the range of the random variable x. Here, x is in the interval 0 < x < 400, so the length of the rectangle's base is Substitute the area and base into the formula for the area of a rectangle to find the height. area = (base)(height) --?-- )(theight) 1 = 1 height = Of interest is the probability that x is at most 300, giving the probability statement P 2- v 300).
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