Fatigue wearout of a component has a log normal distribution with ty = 5000 hours and s = 0.20. %3D (a) Compute the MTTF and SD.
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- solve the problem in the photo using normal distribution lawsX has a standard normal distribution. Derive the mean, variance, cdf and pdf of |X|. Show workingIdentify the probability density function. f(x) = 1/6, [0,6] Find the mean, variance, and standard deviation without integrating. (Round your standard deviation to three decimal places.) Mean = ________________ Variance = _________________________ Standard Deviation (should be in root form) = _________________________
- The useful life of a bicycle bought at Basement-mart fits a log normal distribution with a mean of 17 months and a standard deviation of 10.54 months. Suppose that 96 bicycles are randomly chosen, and let¯¯¯X=the average useful life of a bicycle bought at Basement-mart, from a sample of 96 bicycles (in months).The residual for the first observation in the table is The average value of the residuals isSurface areas of aerosol particles are crucial as they are found to correlate with health effects closely. An aerosol stream generated from a diesel engine has a distribution that is log-normal with a number median diameter of 0.1 μm and a geometrical standard deviation of 2.0. Using the table of normal integrals, determine the fraction of particles by surface area that is contained within the size range from 0.05 to 0.25 μm.
- The undergraduate grade point averages (UGPA) of students taking an admissions test in a recent year can be approximated by a normal distribution, as shown in the figure. (a) What is the minimum UGPA that would still place a student in the top 10 % of UGPAs? (b) Between what two values does the middle 50 % of the UGPAs lie? 3.2642.52Grade point average mu equals 3.26 sigma equals 0.16 x A normal curve labeled mu = 3.26 and sigma = 0.16 is over a horizontal x-axis labeled Grade point average from 2.52 to 4 in increments of 0.37 and is centered on 3.26. (a) The minimum UGPA that would still place a student in the top 10 % of UGPAs is nothing . (Round to two decimal places as needed.) (b) The middle 50 % of UGPAs lies between nothing on the low end and nothing on the high end. (Round to two decimal places as needed.)distributions of both Y1 and Yn are uniform and continuousDetermine moment generation function of the Exponential distribution.
