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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