8. (p.158/# 4.67) Find the Mean of the Random Variable g(x, y) = +X2Y, where the Joint Density Function of X and Y is f(x,y) = (x+2y), 0<<1, 1< y < 2, elsewhere.
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- Let X and Y are two random variables with p.d.f as F(x,y) = 3x^2y+3xy^2,0 < x< 1,0 < y < 1. (i) Find conditional density of X given Y. (ii) Find the mean, mode and standard deviation of r.v Y. (iii) Correlation between X and Y. (iv) Check that X and Y are independent or not?Let X and Y be independent random variables. X is N(1,9) and Y is uniform on the interval {--1, 1]. Lat Write down the joint density for (X,Y) o Give the mean and variance of Y c) Give the median of X I dY Give the correlation coefficient p of X and YLet X and Y be two continuous random variables with joint probability density (3x function given by: f(x.y)%= 0sysxThe density function of two random variables X and Y is ,-2(x+y) fx,r (x, y) =u(x)u(y)4e¯¾x*y) X,Y Find the mean value of the function e-*+),Let X and Y be two continuous random variables with joint probability density [3x function given by: f(x,y)= 0Q4) The probability mass function of Y is f(y) = y/6 for y=1,2,3,4. Find the variance of Y.AsapIf X is a continuous random variable find the CDF and density of the function y = x/3Let X1, X2, ..., X, be independent random variables with the random variable X; having density function TA e, 1>0, fx,(x) = 0, I< 0, where v; E {1,2, ...} and i e {1,2, ..., n}. Using any method that we learned from Chapter 6 of our textbook, find the density function for Xị. 1=1The random variable Y has probability density function f(V) = k(y + y³), 0 2. Hence find PG < Y <). iii) Find the variance of Y.6) The random variables X and Y have joint density f( x, y) = x2-y2 for 1< x, 1s y and f( x, y) = 0 otherwise. %3! Compute the joint density of U = X /Y and V = X Y.X is a uniform random variable over the interval (3, 5). Find the density function of X for the interval (3, 5)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,