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- let x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isFind the mean of the random variable X with PDF S 3x² _if 0Let X be a continuous random variable with a pdf given by f(x) = (3x^2)/2 where x lies in the closed interval [-1,1]. Evaluate P(x>1/2). Select the correct response: 7/16 8/17 2/17 7/8Develop a random variate generator for a random variable X with the pdf if 0let X and Y be independent standard normal random variables. Determine the pdf of W = X^2 + Y^2. Find the mean and the variance of U= (1/2)WLet X and Y be two continuous random variables having joint pdffX,Y (x, y) = (1 + XY)/4, −1 ≤x ≤1, −1 ≤y ≤1.Show that X ^2 and Y ^2 are independent.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,