need help understanding this hw problem 2. Let T(x, y, z) = (x + 2, Y...
2. Let X and Y be two continuous random variables varying in accordance with the joint density function, fx.y(z, y-e(x + y) for 0 < z < y < 1. Solve the following problem s. (1) Find e, fx(a) and fy (v) (2) Find fx-u(z) and fY1Xux(y) (8) Find P(Y e (1/2, 1)|X -1/3) and P(Y e (1/2,2)| X 1/3). 3. Find P(X < 2Y) if fx.y(zw) = x + U for X and Y each defined over the unit...
(b) and (c) are what i need help with Problem(7) Let z Student's t-distribution. The density function of T is Normal(0, 1) and Y ~ xã, then the new r.v. T = Jun has the r[(y + 1)/2) -(4+1)/2 fr(t) = + (7/2) (a) (3 points) Describe the similarity/difference between T and Z. (b) (6 points) Let to be a particular value of t. Use t-distribution table to find to values such that the following statements are true. (Given that...
Let T є L(C3) be defined by T(r, y, z)-(y-2-2c, z-2-2y,1-2y-22). (a) Is span((1,1,1)) invariant under T? (b) Is U = { ( (c) Is U = {(x, y, z) : x + y + z = 0} invariant under T? (d) Is λ 2 an eigenvalue of T? Is T-21 injective? (e) Find all eigenvectors of T associated to the eigenvalue λ =-3. 4. r, y,r-y) : x, y E C} invariant under T?
Let T: R3 → R2 T(x, y, z) = (x + y,y+z) a. Is T a linear transformation? b. Find the matrix A of T C. Find the dimension of NUT and image T
HW on independent rivins I - © Let sa o<x<1 - ocy<x</ f(x,y)= z ó otherwise and the correlation Find Coo (X,Y) coefficient s. X ② Let 8(x, y) -f / 1 e 2 xso, y so otherwise and the correlation Find Coo (X,Y) coefficient s.
(8 points) The temperature at a point (x, y, z) is given by T(x, y, z) = 1300e-x-2y-2? where T is measured in °C and x, y, and z in meters. 1. Find the rate of change of the temperature at the point P(2, -1, 2) in the direction toward the point Q(3,-3,3). Answer: Dp S(2.-1, 2) = 2. In what direction does the temperature increase fastest at P? Answer: 3. Find the maximum rate of increase at P. Answer:
Let X, y, and U be jointly normal zero-mean random variables with variances Problem 1 4, 2, and 1, respectively, such that E XY 1. Assume that U is independent of X and Y Let Z = X + Y + U. Find the joint PDF of X, Y. and Z. Your answer should be explicit C1 and not contain vectors or matrices. Let X, y, and U be jointly normal zero-mean random variables with variances Problem 1 4, 2,...
Al. Let T1(x, y, z) = (1-y+z, 2:0 – y + 2z, 2y + 2). (a). Is T1 one-to-one? (b). Is T onto?
Problem 4. (15 points each) Let F(x, y, z) = (0, x, y) G(x, y, z) = (2x, z, y) + (x, y, z) = (3y, 2x, z). (a) For each field, either find a scalar potential function or prove that none exists. (b) For each field, either find a vector potential function or prove that none exists. (c) Let F(t) = (2, 2t, t2). For which of these vector fields is ñ a flow line? Justify your answer.
Problem 8.7. Let y V4- z2 and f(z) = 2x + 3. Compute the composition %3D = g(x) y = f(g(x)). Find the largest possible domain ce le of x-values so that the composition y = f(g(x)) 't |3D is defined. X-