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 {0² · e-x²1 (20²) f(x; 0) = 8² 0 as a model for the X distribution. x > 0 otherwise (a) Verify that f(x; 0) is a legitimate pdf. √²/27 · e-x2²/1(20²) dx = less than 200 at least 200 =0- (b) Suppose 0 = 144. 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 (c) What is the probability that X is between 100 and 200 (again assuming 0 = 144)? (Round your answer to four decimal places.)
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 {0² · e-x²1 (20²) f(x; 0) = 8² 0 as a model for the X distribution. x > 0 otherwise (a) Verify that f(x; 0) is a legitimate pdf. √²/27 · e-x2²/1(20²) dx = less than 200 at least 200 =0- (b) Suppose 0 = 144. 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 (c) What is the probability that X is between 100 and 200 (again assuming 0 = 144)? (Round your answer to four decimal places.)
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Please solve a, b, c, and d.
![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
X
a-fo
e-x²/(20²)
=
0²
f(x; 0)
0
as a model for the X distribution.
X > 0
otherwise
(a) Verify that f(x; 0) is a legitimate pdf.
X
√²/2² · e-x2²/(202²) dx =
6°
е
0-
0
(b) Suppose 0 = 144. 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 0 = 144)? (Round your answer to four decimal places.)
(d) Give an expression for P(X ≤ x).
P(X ≤ x) =](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7afdb6c4-3a61-4c47-91da-dfd2e9ec1a67%2Fbbeaca94-0ed3-4133-8613-8fbe377bb491%2Fpsu446_processed.png&w=3840&q=75)
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
X
a-fo
e-x²/(20²)
=
0²
f(x; 0)
0
as a model for the X distribution.
X > 0
otherwise
(a) Verify that f(x; 0) is a legitimate pdf.
X
√²/2² · e-x2²/(202²) dx =
6°
е
0-
0
(b) Suppose 0 = 144. 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 0 = 144)? (Round your answer to four decimal places.)
(d) Give an expression for P(X ≤ x).
P(X ≤ x) =
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