Question

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 f(x; ?) = { x/?² ? e??²?(²?²) x > 0 0 otherwise as a model for the X distribution. (a) Verify that f(x; ?) is a legitimate pdf. ??? x/?² ? e??²?(²?²) dx = [ ] ?? = 0 ? ( ) = 1 (b) Suppose ? = 131. 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 ? = 131)? (Round your answer to four decimal places.) (d) Give an expression for P(X ? x). P(X ? 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
f(x; ?) = {
x/?² ? e??²?(²?²)  x > 0
0  otherwise
as a model for the X distribution.
(a) Verify that f(x; ?) is a legitimate pdf.
??? x/?² ? e??²?(²?²) dx = [ ] ??
= 0 ? ( )
= 1
(b) Suppose ? = 131. 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 ? = 131)? (Round your answer to four decimal places.)
(d) Give an expression for P(X ? x).
P(X ? 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
f(x; ?) =
x/?² ? e??²?(²?²) x > 0
0 otherwise
as a model for the X distribution.
(a) Verify that f(x; ?) is a legitimate pdf.
??? x/?² ? e??²?(²?²) dx = [ ] ??
= 0 ? ( )
= 1
(b) Suppose ? = 131. 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 ? = 131)? (Round your answer to four decimal places.)
(d) Give an expression for P(X ? x).
P(X ? x) =

Added by Beverly A.

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