Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel Suppose that X has the following probability density function (called the Rayleigh probability density function). [(x/0²) e-x²/(20²) x > 0 f(x) = 0 otherwise (a) If 0 = 108, find the probability that the vibratory stress is between 95 and 218. (b) If = 108, then 81% of the time the vibratory stress is greater than what value?

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Problem #8: Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel.
Suppose that X has the following probability density function (called the Rayleigh probability density function).
x > 0
f(x) = {(x10²) e-x²7/(20²)
otherwise
(a) If 0 = 108, find the probability that the vibratory stress is between 95 and 218.
(b) If = 108, then 81% of the time the vibratory stress is greater than what value?
Transcribed Image Text:Problem #8: Let X denote the vibratory stress (psi) on a wind turbine blade at a particular wind speed in a wind tunnel. Suppose that X has the following probability density function (called the Rayleigh probability density function). x > 0 f(x) = {(x10²) e-x²7/(20²) otherwise (a) If 0 = 108, find the probability that the vibratory stress is between 95 and 218. (b) If = 108, then 81% of the time the vibratory stress is greater than what value?
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