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- Suppose that n observations are chosen at random from a continuous pdf fY(y). What is the probability that the last observation recorded will be the smallest number in the sample?Let X be a continuous random variable with pdfFind the mean of random variable of X, if X is random variable with pdf f(x) = c(1-x²), -1Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable-X for the right tire and Y for the left tire, with joint pdf f(x, y) ĮK(x? + y?) 21 25). (Round your answer to three decimal places.) P(Y > 25) = (c) If the pressure in the right tire is found to be 22 psi, what is the expected pressure in the left tire, and what is the standard deviation of pressure in this tire? (It is known that K = Round your answers to two decimal 410,600 places.) expected pressure psi standard deviation psiLet X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X be the lifetime (measured in hours) of an electronic device. suppose thatX let X be a continuous random variable with pdf f(x) = k/x^n, 2000 ≤ x ≤ 10000(a) For n in general, find k. (1.5)(b) What is the probability that the device fails before 5000 hours have passed? Compare the resultsDevelop a random variate generator for a random variable X with the pdf if 0A continuous random variable X has a pdf of the form: f(x) = (562/803) x^3, for 1.66A continuous random variable X has a pdf of the form: f(x) = (824/9) x^2, for 0.01 < X < 0.32. Calculate the standard deviation (sigma) of X.SEE MORE QUESTIONSRecommended textbooks for youCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Calculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,