Suppose X andY are two random variables withE[X]=1,Var(X)=4,E[Y]=−1,Var(Y)=4,andCov(X,Y)=1. Find: (a) correlation between X and Y . (b) Var(X −Y).
Suppose X andY are two random variables withE[X]=1,Var(X)=4,E[Y]=−1,Var(Y)=4,andCov(X,Y)=1. Find: (a) correlation betwee...
For the random variables X and Y having E(X) = 1, E(Y) = 2, Var (X) = 6, Var (Y) = 9, and Pxy = -2/3. Find a) The covariance of X and Y. b) The correlation of X and Y. c) E(X2) and E(Y2).
solution please 2. If X and Y are two random variables with Var(X) = 36, Var(Y) = 16, and Cov(X,Y) = 24, what is ρXY, the correlation coefficient between X and Y? (A) -1 (B) 0 (C) 1/24 (D) 1
6 Suppose that X and Y are random variables such that Var(X)-Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y + 2)
Suppose XX and YY are independent random variables for which Var(X)=7Var(X)=7 and Var(Y)=7.Var(Y)=7. (a) Find Var(X−Y+1).Var(X−Y+1). (b) Find Var(2X−3Y)Var(2X−3Y) (c) Let W=2X−3Y.W=2X−3Y. Find the standard deviaton of W.W.
5. Suppose X and Y are random variables such that E(X)=E(Y) = θ, Var(X) = σ and Var(Y)-吆 . Consider a new random variable W = aX + (1-a)Y (a) Show that W is unbiased for θ. (b) If X and Y are independent, how should the constant a be chosen in order to minimize the variance of W?
6 Suppose that X and Y are random variables such that Var(X) Var(Y)-2 and Cov(x,y)- 1. Find the value of Var(3.X-Y+2)
6. Suppose that X and Y are random variables such that Var(X)=Var(y)-2 and Cov(x,y)-1. the value of Var(ax-y-2). Find
4. Consider two independent random variables X and Y, such that E[X] = 1 E[Y] = 2 var(X) = 2 var(Y) = 1 Let Z = X-Y 2 (a) Calculate E[2] (b) Calculate var(Z). 3
1. Two normal random variables X and Y are jointly distributed with Var(X) 25 and Var(Y) 1600. It is known that P(Y>80| X = 50) 0.1 and P(Y 22 X 40) 0.7886 (1) What is the correlation coefficient between X and Y? (2) What is the expected value of Y given X 50?
der two independent random variables X and Y with the following 11. Consi means and standard deviations: = 60; ơv_ 15. (a) Find E(x + Y), Var(X + Y), E(X Y), Var(X - Y). (b) If x* and Y* are the standardized r.v.'s eorresponding to the r.v.'s X and Y, respectively, determine E(X* + Y*), E(X*-Y*), Var(X* Y*), Var(x* - Y*) der two independent random variables X and Y with the following 11. Consi means and standard deviations: = 60;...