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 xe-x2 (202) X>0 f(x; 0) = 82 otherwise as a model for the X distribution. (a) Verify that f(x; 0) is a legitimate pdf. 1.0. X .e e-x²/(20²) dx = 82 0 =0- (b) Suppose 8 = 127. 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 = 127)? (Round your answer to four decimal places.) (d) Give an expression for P(X ≤ x). P(X ≤ x) = 8
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 xe-x2 (202) X>0 f(x; 0) = 82 otherwise as a model for the X distribution. (a) Verify that f(x; 0) is a legitimate pdf. 1.0. X .e e-x²/(20²) dx = 82 0 =0- (b) Suppose 8 = 127. 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 = 127)? (Round your answer to four decimal places.) (d) Give an expression for P(X ≤ x). P(X ≤ x) = 8
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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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
-x²/(28²)
x > 0
f(x; 8) = 8²
otherwise
as a model for the X distribution.
(a) Verify that f(x; 0) is a legitimate pdf.
00
-x²/(20²)
1.0.
dx =
8²
0
= 0-
(b) Suppose 8 = 127. 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 = 127)? (Round your answer to four
decimal places.)
(d) Give an expression for P(X ≤ x).
P(X ≤ x) =
e
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