6. (a) If W(x, y)- F(u(x, u)) and W,(2,1) 24, u(2,1) 3, ux(2,1)4, uy(2,1) 6, find F(3). (b)I z2ze...
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.
Given the system x'=y+ux and y'= -x + uy - x2y, with u representing the greek letter mu: a) Show that the origin is a fixed point b) Linearize the system near the fixed point and determine the eigenvalues c) Show that a bifurcation exists at u=0 and determine the behavior of the fixed point for u<0, u=0, and u>0
Random variable X has mean Ux=24 and standard deviation σx =6. Randon variable Y has mean Uy =14 and standard deviation σY = 4. A new random variable Z was formed, where Z=X+Y. What can we conclude about X, Y, and Z with certainty? That is, which one is true?
3 U + tyy = 0. 3. Find the directional derivative of f(x,y) 2In y at the point P(2,1) in the direction ū= 21+ 4. Find the linearization of f(x,y) = x2 + y2 at the point P(3, 4) and use it to
Solve the system Ux = y for x. U = ? X = ? If the nxn matrix A can be expressed as A = LU, where L is a lower triangular matrix and U is an upper triangular matrix, then the system Ax = b can be expressed as LUX = b and can be solved in two steps: Step 1. Let Ux = y, so that LUX = b can be expressed as Ly = b. Solve this...
A) Let utility over 2 goods be defined as U(x,y)=x+xy+y. Find the MRS by implicitly solving for y (hint: set U=k) and calculate -dy/dx. B) Now find the MRS by using MRS =Ux/Uy.
I need all details. Thx 9. Consider a basis B = {bi, b2} of a sulspoo, W of R4 where -3 (a) Determine the coordinates of x(3,-1,-2,1) in the basis B (i.e. fnd x). (b) Suppose that bl el-C2 and b2 2c1 +c2. Determine the coordinates of x = (3.-1,-21) in the basis C = {c,,c) (i.e. find [x le) (e) Suppose t dbb an d2b 3b s D- di da a basis of W Why or why not? 9....
(3) Consider f: R3- R3 defined by (u,, w)-f(r, y, :) where u=x w = 3~. Let A = {1 < x < 2, 0 < xy < 2, 0 < z < 1). Write down (i) the derivative Df as a matrix (ii) the Jacobian determinant, (ii) sketch A in (x, y. :)-space, and iv) sketch f(A) in (u. v, w)-space.
use partial derivative to solve for uf(x,y,t) if f(x,y,t) is 5X^3y-1/xy+1/xt+x^2t^2 Ux=0.5 Uy=0.2 Uz=0.3 Use numerical methos to solve also this problem
Let a. Find at (2,1) b. Find the directional derivative of f at (2,1) in the direction of -i+3j f(:,y) = xy - 1 We were unable to transcribe this image