Two random variables X and Y have means E[X] = 1 and E[Y] = 0, variances...
Two random variables, X and Y, have the following variances: σ,-9 and σ-25 . If their correlation coefficient is 0.5, determine the following 5. (a) the variance of the random variable W 2X+ 3Y b) the variance of the random variable U-3X- Y
3-3.3 Two independent random variables, X and Y, have Gaussian probability density functions with means of 1 and 2, respectively, and variances of 1 and 4, respectively. Find the probability that XY > 0. 3-3.3 Two independent random variables, X and Y, have Gaussian probability density functions with means of 1 and 2, respectively, and variances of 1 and 4, respectively. Find the probability that XY > 0.
9. Let X and Y be two random variables. Suppose that σ = 4, and σ -9. If we know that the two random variables Z-2X?Y and W = X + Y are independent, find Cov(X, Y) and ρ(X,Y). 10. Let X and Y be bivariate normal random variables with parameters μェー0, σ, 1,Hy- 1, ơv = 2, and ρ = _ .5. Find P(X + 2Y < 3) . Find Cov(X-Y, X + 2Y) 11. Let X and Y...
-1 1 9. Suppose the discrete random variables X and Y are jointly distributed according to the following table: 0 0.1 0.1 0.1 3 0 0.2 0.1 4 0.2 0.1 0.1 2x 1 a. Compute the expected values E(X) and E(Y), variances V(X) and V(Y), and covariance Cov(X,Y) of X and Y. [11] b. Let W = X – Y. Compute E(W) and V(W). [4]
If the random variables X, Y, and Z have the means ji x = 3, My = -2, and uz = 2, the variances of = 3, o = 3, o2 = 2, the covariances cov(X,Y) = -2, cov(X, Z) = -1, and cov(Y,Z) = 1, U = Y - Z, and V = X - Y + 2Z. (a) Find the mean and the variance of U and V. (b) Find the covariance of U and V.
Let X1 and X2 be independent random variables with means μ1 and μ2, and variances σ21 and σ22, respectively. Find the correlation of X1 and X1 + X2. Note that: The covariance of random variables X; Y is dened by Cov(X; Y ) = E[(X - E(X))(Y - E(Y ))]. The correlation of X; Y is dened by Corr(X; Y ) =Cov(X; Y ) / √ Var(X)Var(Y )
If the random variables X, Y, and Z have the means ux = 3, uy = -2, and uz = 2, the variances o = 3, o = 3, o2 = 2, the covariances cov(X,Y) = -2, cov(X, Z) = -1, and cov(Y,Z) = 1, U = Y - Z, and V = X - Y +2Z. (a) Find the mean and the variance of U and V, respectively. (b) Find the covariance of U and V.
2. Let X and Y be jointly Gaussian random variables. Let ElX] = 0, E[Y] = 0, ElX2-4. Ey2- 4, and PXY = [5] (a) Define W2x +3. Find the probability density function fw ( of W. [101 (b) Define Z 2X - 3Y. Find P(Z > 3) 5] (c) Find E[WZ], where W and Z are defined in parts (a) and (b), respectively.
Question 19 Consider two random variables X and Y with E(X)= 4, E(Y) = 2, E(XY) = 12, V(X) = 16 and V(Y) = 25, then the correlation coefficient between X and Y is: a. -0.2 b. -0.3 c. 0.2 d. 0.3 e. None of the above need step by step distribution~
Extra: Let X, Y, Z be results of three independent tosses of a fair die. (a) Find the covariance of the random variables W=2X-3Y + Z (b) Find the correlation coefficient of W and V. and V=X-2Y-Z