2 0 -1 EIX) = μ = | 0 | and var(X) Σ _ | 0 -1 0.5 3 0.5 | compute: (a) E[Xi +Xs] (c) var(X2- X3) d var(X2 + X) (e) cov(4X2 +X1,3Xi -2X)
Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 3 1 0.5 1 E [X]-μ | 0 | and var(X)=Σー| 0 0.5 | com pute: 2 c) var(X2-X3 (d) var(X2 + X3) (e) cov(4X2 +X1,3Xi - 2X3)
how to calculate cov(x1,x2), cov(x2,x3),cov(x3,x1)? and how to calculate var(x1),var(x2),var(x3)? Given three random variables Xi, X2, and X such that X[Xi X2 X 20 -1 E [X] ,1-10 | and var(X)=Σ-| 0 3 0. 1 0.5 1 compuite: 2
Given three random variables Given three random variables Xi, X2, and X such that X[Xi X2 Xa, 2 1 0.5 1 (a) EX, + c) var(X2- X3 (d) var(X2 + X3) (e) cov(4X2 +X1,3Xi - 2X3)
Let X and Y be random variables with the follow E(Y) μ,--2 Var(x) o, 0.3 Var(Y)-σ,-0.5 Cov(XY) o,,-0.03 Find the following: ESX-3 Y)
1 [3]. Let X1,X2, X3 be iid random variables with the common mean --1 2-4 and variance σ Find (a) E (2X1 - 3X2 + 4X3); (b) Var(2X1 -4X2); (c) Cov(Xi - X2, X1 +2X2).
5.26 Suppose that y is N, (μ, 2), where μ LJ and -σ2ρ for all Thus E(yi-μ for all i, var(yi) 0" for all i, and cov(yoy ij; that is, the y's are equicorrelated. (a) Show that Σ can be written in the form Σ-σ2(I-P)1+a (b) Show that Σ-i(vi-y?/(r2(1-p] is X2(n-1) 5.26 Suppose that y is N, (μ, 2), where μ LJ and -σ2ρ for all Thus E(yi-μ for all i, var(yi) 0" for all i, and cov(yoy ij; that...
problems binomial random, veriable has the moment generating function, y(t)=E eux 1. A nd+ 1-p)n. Show that EIX|-np and Var(X) np(1-p) using that EIX)-v(0) nd E.X2 =ψ (0). 2. Lex X be uniformly distributed over (a b). Show that ElXI 쌓 and Var(X) = (b and second moments of this random variable where the pdf of X is (x)N of a continuous randonn variable is defined as E[X"-广.nf(z)dz. )a using the first Note that the nth moment 3. Show that...
= = 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, Let Var(X1) = Var(X3) = 2, Var(X2) Cov(X1, X3) = -1. i) Suppose Y1 = X1 - X2. Find Var(Y1). ii) Suppose Y2 = X1 – 2X2 – X3. Find Var(Y2) and Cov(Yı, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fxı,Y,(y1, y2). iii) Suppose Y3 = X1 + X2 + X3. Compute the covariance...
3. You may use this fact throughout: For any scalars a, a2,a3 and random variables .X2, X3: (a) If Cov (Xi, X2) Cov (X2, X3)-p, Cov (Xi, X3)-p and Var(X1,2,3, then write the 3 x 3 covariance matrix of the random vector X = (X1,X2,X3). (b) Compute Var(Xi X2+X3) when p 0.6. (e) Mark is interested in forecasting X using the linear predictor &bbX He realizes the forecast error is X - X X bX2 -bX and a great way...