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- Let 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{OSuppose that two continuous random variables X and Y have joint probability density function fxy = 1sxs2,0sy<3 elsewhere Find the strength of the relationship and interpret the findings.Let X be a random variable with uniform distribution on the interval [-2,2]. Let Y be defined as Y = X5. Calculate the pdf of Y.Let X be a continuous random variable with PDF 3 x > 1 x4 fx(x) = otherwise Find the mean and variance of x.Let X ~ Uniform(a, b). Find Expected value EX.2) Let X be a continuous random variable with PDF 0The continuous random variable XX has a probability density function (pdf) given by Part(d) Find Var(X), correct to 2 decimal places Part(e) Find the median of X, correct to 2 decimal places.Part(f) Find E(X), correct to 2 decimal placesQ4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.Use the geometric distribution to derive E(Y), E(Y^2), and V(Y) from the Poisson distributionSuppose two independent continuous random variables X, Y have exponential distribution with mean 0. a) Write the joint probability density function. b) Express F (2) = P( < z) using integrals and compute the integrals. c) Calculate the PDF of Z = Y/X as f(x) = F' (2) d) Compute the expected value and the variance of Z, if they exist.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 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.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,