02'e-x/(20²) dx = | 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/(282) x > 0 f(x; 0) = { e2 otherwise as a model for the X distribution. (a) Verify that f(x; 0) is a legitimate pdf. × ) = 0 - = 1 (b) Suppose e 119. 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 Enter a number. at least 200 (c) What is the probability that X is between 100 and 200 (again assuming e = 119)? (Round your answer to four decimal places.) (d) Give an expression for P(X < x). P(X s x) = 1- e

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Author:Amos Gilat
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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
ex?/(282)
02
x > 0
f(x; ө) %3D
otherwise
as a model for the X distribution.
(a) Verify that f(x; 0) is a legitimate pdf.
e-x2/(282) dx =|
02
:)
= 0 -
= 1
(b) Suppose = 119. 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
Enter a number.
at least 200
(c) What is the probability that X is between 100 and 200 (again assuming 0 = 119)? (Round your answer to four decimal places.)
(d) Give an expression for P(X < x).
P(X < x) =
1- e
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 ex?/(282) 02 x > 0 f(x; ө) %3D otherwise as a model for the X distribution. (a) Verify that f(x; 0) is a legitimate pdf. e-x2/(282) dx =| 02 :) = 0 - = 1 (b) Suppose = 119. 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 Enter a number. at least 200 (c) What is the probability that X is between 100 and 200 (again assuming 0 = 119)? (Round your answer to four decimal places.) (d) Give an expression for P(X < x). P(X < x) = 1- e
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