3) Let (x, y), (X2, y2), and (X3. Y3) be three points in R2 with X1...
iii. If the vertices of a triangle, in counterclockwise order are (x1.yı), (X2,Y2) and (x3 ,Y3), Show that the area of the triangle is A= }((x, y, – x, y;)+(x,y; – x, y,)+(x; y; – x, y,)). [5%) iv. Use Part iii to find the area of the triangle with vertices (0,0); (2,0) and (0,2), then, check the result geometrically. [5%)
= = 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...
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...
Write a program that prompts the user to enter three points (x1, y1), (x2, y2), (x3, y3) of a triangle and displays its area. The formula for computing the distance of two points (x1, y1) and (x2, y2) is d = Math.sqrt((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1)); or d = Math.pow((x2 - x1) * (x2 - x1) + (y2 - y1) * (y2 - y1), 0.5); The formula for computing the...
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 =...
(a) Show that the points (x1, yı), (X2, y2), ..., (xn, yn) are collinear in R2 if and only if 1 X1 yi X2 Y3 rank < 2 1 Xn yn ] (b) What is the generalization of part (a) to points (x1, Yı, zı), (x2, y2, 22), ...,(Xn, Yn, zn) in R'. Explain.
с раиси от к. Show that the function that takes ((X1, X2, X3), (y1, y2, y3)) E to xi yi + x3y3 is not an inner product on R. ((X1, X2, X3), (y1, y2, y3)) E R3 x R3 von SE
determine whether or not the equations represent y as a function of x y=x3-X X2-Y2=1 X3+Y3=4
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...
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.