Let X denote the vibratory stress (psi) on a wind tur- bine blade at a particular wind speed in a wind tunnel. The article "Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar Energy Engr., 1982: 107–111) proposes the Rayleigh distribution, with pdf e-x?/(202) 02 x>0 f(x; 0) = otherwise as a model for the X distribution. a. Verify that f(x; 0) is a legitimate pdf. b. Suppose 0 = 100 (a value suggested by a graph in the article). What is the probability that X is at most 200? Less than 200? At least 200? с. What is the probability that X is between 100 and 200 (again assuming 0 = 100)? d. Give an expression for P(X < x).

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Let X denote the vibratory stress (psi) on a wind tur-
bine blade at a particular wind speed in a wind tunnel.
The article "Blade Fatigue Life Assessment with
Application to VAWTS" (J. of Solar Energy Engr., 1982:
107-111) proposes the Rayleigh distribution, with pdf
e-x²/(20)
x> 0
f(x; 0) = { 0²
0.
otherwise
as a model for the X distribution.
a. Verify that f(x; 0) is a legitimate pdf.
b. Suppose 0 = 100 (a value suggested by a graph in
the article). What is the probability that X is at most
200? Less than 200? At least 200?
с.
What is the probability that X is between 100 and 200
(again assuming 0 = 100)?
d. Give an expression for P(X< x).
Transcribed Image Text:Let X denote the vibratory stress (psi) on a wind tur- bine blade at a particular wind speed in a wind tunnel. The article "Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar Energy Engr., 1982: 107-111) proposes the Rayleigh distribution, with pdf e-x²/(20) x> 0 f(x; 0) = { 0² 0. otherwise as a model for the X distribution. a. Verify that f(x; 0) is a legitimate pdf. b. Suppose 0 = 100 (a value suggested by a graph in the article). What is the probability that X is at most 200? Less than 200? At least 200? с. What is the probability that X is between 100 and 200 (again assuming 0 = 100)? d. Give an expression for P(X< x).
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