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 pdfe-x²/(20²)f(x; 8) = 820as a model for the X distribution.X>0otherwise(a) Verify that f(x; 6) is a legitimate pdf.[ -= 2 · 0-× ² / (20²) dx =:0DO0(b) Suppose 8 = 124. What is the probability that X is at most 200? Less than 200? At least 200? (Round your answer to four decimal places.)at most 200less than 200at least 200(d) Give an expression for P(X ≤ x).P(X SX) =(c) What is the probability that X is between 100 and 200 (again assuming 6 = 124)? (Round your answer to four decimal places.)

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

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Q3. Exponential Distribution has a memoryless property. Intuitively, it means that the probability of customer service answering you call (assuming waiting time is exponential) in the next 10 mins is the same, no matter if you have waited an hour on the line or just picked up the phone. Formally, if X ∼ exponential(λ), f(x) = λ exp(- λx), and t and s are two positive numbers, use the definition of conditional probability to show that P(X > t + s | X > t) = P(X > s).Hint: Find the cdf of X first, and note that P(X > t + s Ç X > t) = P(X > t + s)
Suppose X has a binomial distribution with p = 0.3 and n = 10. Compute P(X=0), P(X=2), E(X) and VarX.
arn.squ.edu.om/mod/quiz/attempt.php?attempt=1766808&cmid=8751228&page=D21 SYSTEM (ACADEMIC) s Statistics 1 || Spring21 Time left 0: Suppose a company produces lightbulbs with a mean lifetime of 1000 hours and a standard deviation of 50 hours. So, the z-score for a particular lightbulb that lasts for only 700 hours is a. 300 b. 6
(a) Let Z follow a standard normal distribution. i. Find the equi-tailed 95% probability interval, i.e. find a > 0 such that P(Z € (-a, a)) = 0.95 and express your result in terms of the inverse function -1 of the standard normal cdf (note that the inverse function satisfies -((x)) = x for all r E R). Finally write down the value of a to three significant digits. ii. Instead of an equi-tailed interval, consider the interval (-a, b) where a, b >0 are such that P(ZE (-a, b)) = 0.95. Express b as a function b(a) of a. It may help to express your results in terms of -1 and . Show that the derivative of the length I of the interval, I = b(a) + a, is given by dl = 1 da (a) (-(0.95+ (-a))' where o denotes the standard normal pdf. Hence obtain a candidate value of a for which the length of the interval is minimal by equating this derivative to zero. You do not need to show that this candidate value is an actual minimizer.
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a. What is the probability that it would take more than 4 minutes to reach the accident? b. What is the probability that it would take either less than 2 minutes or more than 5 minutes to reach the scene of the accident? c. What is the expected time to reach the accident?
Bapu
Consider the distribution of Binomial, Poisson, Exponential, Gamma, and let T1=X+4 and T2=(X-1) Check the property of biasdness
4.111 Work with a transformation. Here is a probability distribution for a random variable X: lls balls. Value of X T Probability 3 0.4 7 T 0.6 2011 (a) Find the mean and the standard deviation of this distribution. 80 21000 ried to thod isdı 29ilqıni zniT (b) Let Y = 4X - 2. Use the rules for means and variances to find the mean and the standard deviation of the distribution of Y. (c) For part (b), give the rules that you used to find your answer.
1. Let XX represent the full height of a certain species of tree. Assume that XX has a normal probability distribution with a mean of 231.1 ft and a standard deviation of 5.6 ft.A tree of this type grows in my backyard, and it stands 230 feet tall. Find the probability that the height of a randomly selected tree is as tall as mine or shorter.P(X<230) = Enter your answer accurate to 4 decimal places. 2. Assume that z-scores are normally distributed with a mean of 0 and a standard deviation of 1.If P(−0.7<z<b)=0.7352P find b.b= (Round to two decimal places.) Do not round until the very last step. Any intermediate steps should include all decimal places.
3. Fill in the blank spaces of table B1 using information compiled in table B. Table B Breusch-Godfrey Serial Correlation LM Test: Prob. F(2,55) Prob. Chi-Square(2) F-statistic 11.70006 0.0001 Obs*R-squared 17.90823 0.0001 Table B1: Breusch-Godfrey Serial Correlation LM Test F-statistic: Probability: a. Write down the null and alternative hypotheses underlying Breusch-Godfrey serial correlation (autocorrelation) test. b. Will you accept or reject the null hypothesis based on the Breusch-Godfrey test for residual autocorrelation? Why or why not?
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