Problem #8: Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Suppose that X has the following probability density function (called the Rayleigh probability density function). f(x) = (x/0²) e-x²/(20²) x > 0 0 otherwise (a) If = 96, find the probability that the vibratory stress is between 83 and 375. (b) If = 96, then 80% of the time the vibratory stress is greater than what value?
Problem #8: Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Suppose that X has the following probability density function (called the Rayleigh probability density function). f(x) = (x/0²) e-x²/(20²) x > 0 0 otherwise (a) If = 96, find the probability that the vibratory stress is between 83 and 375. (b) If = 96, then 80% of the time the vibratory stress is greater than what value?
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Problem #8: Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel.
Suppose that X has the following probability density function (called the Rayleigh probability density function).
Problem #8(a):
Problem #8(b):
f(x) =
S (x10²) e-x2²/(20²) x > 0
o
otherwise
(a) If 0 = 96, find the probability that the vibratory stress is between 83 and 375.
(b) If = 96, then 80% of the time the vibratory stress is greater than what value?
Round your answer to 4 decimals.
round your answer to 2 decimals
Expert Solution
Step 1
Given density function,
a)
If ,
Consider,
The probability that the vibratory stress is between 83 and 375 is,
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