Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a windtunnel. The article “Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar EnergyEngr., 1982: 107–111) proposes the Rayleigh distribution, with pdf{*-a² /(20²)x > 0•ef(x; 0) =otherwiseas 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 atmost 200? Less than 200? At least 200?c. What is the probability that X is between 100 and 200 (again assuming 0 = 100)?d. Give an expression for P(X < æ).

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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. The article “Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar Energy Engr., 1982: 107–111) proposes the Rayleigh distribution, with pdf

Let X denote the vibratory stress (psi) on a wind turbine 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

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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. The article “Blade Fatigue Life Assessment with Application to VAWTS" (J. of Solar Energy
Engr., 1982: 107–111) proposes the Rayleigh distribution, with pdf
{*
-a² /(20²)
x > 0
•e
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?
c. What is the probability that X is between 100 and 200 (again assuming 0 = 100)?
d. Give an expression for P(X < æ).

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