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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 {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)
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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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) =
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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