Let X denote the power (MW) generated by a wind turbine at a given wind speed. The article “An Investigation of Wind Power Density Distribution at Location With Low and High Wind Speeds Using Statistical Model” (Appl. Energy 2018: 442–451) proposes the Rayleigh distribution, with pdf

as a model for the X distribution. The value of the parameter θ depends upon the prevailing wind speed.
a. Verify that ƒ(x; θ) is a legitimate pdf.
b. Suppose θ = 100. 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 θ = 100)?
d. Give an expression for the cdf of X.

Transcribed Image Text:

X f(x; 0) 1 - 10/²2 - e-x²/(20²) 0 < x