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 e-x²/(26²) -fo f(x; 0) as a model for the X distribution. x>0 otherwise (a) Verify that f(x; 8) is a legitimate pdf. 12/27 - 0²/1(21²) d dx= -0- (b) Suppose 8 - 116. What is the probability that X is at most 200? Less than 200? At least 2007 (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 - 116)? (Round your answer to four decimal places.) (d) Give an expression for P(X s X). P(X ≤ x) =

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