= = 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...
I need the solution of this question asap 3, Cov(X1, X2) = 2, Cov(X2, X3) = -2, 5. 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(Y1, Y2). Assuming that (X1, X2, X3) are multivariate normal, with mean 0 and covariances as specified above, find the joint density function fyy, y,(91, y2). iii) Suppose Y3 =...
Let Y1, Y2, and Y3 be independent, N(0, 1)-distributed random variables, and set X1 = Y1 − Y3, X2 = 2Y1 + Y2 − 2Y3, X3 = −2Y1 + 3Y3.Determine the conditional distribution of X2 given that X1 + X3 = x.
Q2 Suppose X1, X2, X3 are independent Bernoulli random variables with p = 0.5. Let Y; be the partial sums, i.e., Y1 = X1, Y2 = X1 + X2, Y3 = X1 + X2 + X3. 1. What is the distubution for each Yį, i = 1, 2, 3? 2. What is the expected value for Y1 + Y2 +Yz? 3. Are Yį and Y2 independent? Explain it by computing their joint P.M.F. 4. What is the variance of Y1...
Consider the following equations: y1 = a1y2 +a2y3 +x1 +x2 +e1 (1) y2 = by1+2x3+x1+e2 (2) y3 =cy1+e3 (3) Here a1, a2, b, c are unknown parameters of interest, which are all posi- tive. x1, x2, x3 are exogenous variables (uncorrelated with y1, y2 or y3). e1, e2, e3 are error terms. (a) In equation (1), why y2,y3 are endogenous? (b) what is (are) the instrumental variable(s) for y2, y3 in equation (1)? (no need to explain why) (c) In...
3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1 < x2 < X3. Suppose that y = ax + by + c is a parabola passing through the three points (x1, yı), (x2, y), and (x3, Y3). We have that a, b, and c must satisfy i = ax + bx + C V2 = ax + bx2 + c y3 = ax} + bx3 + c Let D = x X2 1....
Suppose you are given the following feature vectors: x1 = (1,0), x2 = (4,2), x3 = (0,-1), x4 = (-1,-1), x5 = (-2,1) Their corresponding labels are y1 = 1, y2 = 1, y3 = -1, y4 = -1, y5 = -1 Note: there is no bias term in this problem. Suppose we run perceptron on this dataset starting with w0 = (0,0). Write down the values of w1,w2,w3,w4 and w5 after each training instance, that is, wi is the...
Consider two independent random samples, X1, X2, X3, X1 and Y1, Y , Y3, 74, Y5, Y, each from the same population having unknown mean and unknown variance ,2. Consider the set of estimators for p given by S{A} = {ña :fla = (1 - a) X+ay, for 0 <a<1}. What is the value of a, denoted by a*, such that file has the lowest mean square error of all available estimators in S{n} ? Answer:
Set A contains three numbers x1, x2 and x3. Set B contains four numbers y1, y2, y3 and y4. These two sets have the following characteristics: Set Mean Standard deviation A 10 2 B 45 5 Set X consists of the following eight numbers: u1 =70, u2 =7x1, u3 =7x2, u4 =7x3, u5 =2y1, u6 =2y2, u7 =2y3, u8 =2y4. Find the mean and standard deviation of the numbers in set X.
matlab 3. Filename: area2d.m The area of a triangle whose three vertices are points (x1, yı), (X2, y2), and (x3, y3) can be found using the absolute value of the following equation: A = 3 [x: (– yz) – x2\1 – yz) + x3V1 – Yz)] Write a MATLAB function area2d that calculates the area of a triangle using the following syntax: A = area2d (x,y) where x and y are vectors such that x = [X1, X2, X3] and...