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- Find the mean of the random variable X with PDF S 3x² _if 0Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)Develop a random variate generator for a random variable X with the pdf if 0Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Find the variance of the random variable X with a PDF given by 3x2 S* if - 1< x< 1, f(x) = 2 otherwise. Submit your answer in fractional form.Let 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 7/8Let X and Y be independent Exp(2) random variables. Define W = X + Y. a) Determine the correlation between X and W. The joint pdf of X and W is: fx,w(x, w) = 1^(2) e^(-1w) I{Olet k be a random variable that takes with equal prob 1/(2n+1), values in integer the interral' [-n, n]. Find the PMF of the random variable y = log (x) where X = a¹" and a>o.2) Let X be a continuous random variable with PDF 0The weekly demand for propane gas (in 100's of gallons) from a particular facility is a random variable X with pdf: f(x) = 2(1) for 1 ≤ x ≤ 2 Please find out the mean of X. 3/2-In(2) 3-2 In(2) 1/2-In(4) 3-In(2)We have a random variable X that is uniformly distributed on interval [-1,2]. Let Y = |X| - 1. We want to find pdf using CDF technique. What is the support and pdf for the random variable Y? What would fy(-.2) be? What about Fy(-.2) be?let 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)WSEE 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,