Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Use the Rayleigh distribution, with pdf. e-x²/(20²) f(x; 8) 82 0 as a model for the X distribution. (a) Verify that f(x; 8) is a legitimate pdf. 82 X>0 otherwise. e 0 (b) Suppose 8 124. What is the probability that X is at most 200? Less than 200? At least 200? (Round your answer to four decimal places.) at most 200 less than 200 at least 200 (c) What is the probability that X is between 100 and 200 (again assuming 8 124)? (Round your answer to four decimal places.) (d) Give an expression for P(X s X). P(XS X) =
Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Use the Rayleigh distribution, with pdf. e-x²/(20²) f(x; 8) 82 0 as a model for the X distribution. (a) Verify that f(x; 8) is a legitimate pdf. 82 X>0 otherwise. e 0 (b) Suppose 8 124. What is the probability that X is at most 200? Less than 200? At least 200? (Round your answer to four decimal places.) at most 200 less than 200 at least 200 (c) What is the probability that X is between 100 and 200 (again assuming 8 124)? (Round your answer to four decimal places.) (d) Give an expression for P(X s X). P(XS X) =
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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Transcribed Image Text:Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Use the Rayleigh distribution, with pdf
e-x²/(20²)
f(x; 8) = 82
0
as a model for the X distribution.
X>0
otherwise
(a) Verify that f(x; 6) is a legitimate pdf.
[ -= 2 · 0-× ² / (20²) dx =
:0
DO
0
(b) Suppose 8 = 124. What is the probability that X is at most 200? Less than 200? At least 200? (Round your answer to four decimal places.)
at most 200
less than 200
at least 200
(d) Give an expression for P(X ≤ x).
P(X SX) =
(c) What is the probability that X is between 100 and 200 (again assuming 6 = 124)? (Round your answer to four decimal places.)
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