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- Consider a random variable Y with PDF Pr(Y=k)=pq^(k-1),k=1,2,3,4,5....compute for E(2Y)the random variable Y is such that : E(2Y+3)=6 and Var(2-3Y)=11 find E(Y^2)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{OLet 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.Find the mean of the random variable X with PDF S 3x² _if 0Determine the expected value of g(x,y) = (X^3)+(Y^2)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)Wlet x be a random variable with moment generating function Mx(t)=(0.6 + 0.4e^t)^20 then the variance of x isThe density of a random variable X is f(x) = C/x^2 when x ≥ 10 and 0 otherwise. Find P(X > 20).calculate the variance of g(X) =X^2+2, where X is the random variable with probability distribution : x=0,1,2,3; f(x) = 0.1, 0.2, 0.4,0.3 . a. 19.65 b. 26.28 c. 10.65 d. 11.65 e. 14.65Let the probability function of the random variable X be defined as f(x)=c/x^4 for x>1, otherwise f(x)=0. Calculate the constant c, the expected value and the variance.Suppose that f(x)=k/(4^x), x=1,2,3,... is the probability function for a random variable X. Find the value of 1/k.SEE MORE QUESTIONSRecommended textbooks for youAlgebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageCalculus For The Life SciencesCalculusISBN:9780321964038Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.Publisher:Pearson Addison Wesley,