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 > 0f(x)=10otherwise(a) If = 108, find the probability that the vibratory stress is between 82 and 361.(b) If = 108, then 92% of the time the vibratory stress is greater than what value?

Answered: Let X denote the vibratory stress (psi)…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Let X be a random variable that follows the beta distribution. This random variable is continuous and is defined over the interval from 0 to 1. The probability density function is given by whereand are integers, whose values determine the shape of the probability density function. Because X varies between 0 and 1, we can think of X as the probability that some event (say) E occurs or the proportion of times an event occurs in some population. For example, E could denote the event that a critical part in a newly designed car will lead to a catastrophic failure in accidents at high speeds. The expected value (i.e., mean) of this random variable is []. That is, . The Excel commands for the beta random variable are =beta.dist(x,,,true,0,1) for the cumulative probability distribution, and =beta.dist(x,,,false,0,1) for the probability density function. (a) Now, think in Bayesian terms.…

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