o X-Z S SE -22 e 2 1 e Shoold equel o X-Z S SE -22 e 2 1 e Shoold equel
2) For the given equations: V(z) = { é o se} V(,0) = V $(x) + V1() + vee(r) a) Write the expression for 4A (x,t). b) What is the expectation value for (E) ? Write the expression in E.. c) Write the expression for W.(x,t) at E2 for t>t, and what is the probabilities at t2 > ti d) Write the another expression for WB(x, 0) with the same value of (E). e) Write the another expression for c(x,0)...
Consider the function f and region E. f(x, y, z) = y, E = {(x, y, z)| 1 5 x2 +3? 59,0 SyS 1 - x2 - 22; (a) Express the region E in cylindrical coordinates. O E = {(r, 0, 2)Iisrs9,0 SO S 21,0 S 231-23 O E = {(1, 0, 2)| 1 575 3,0 SOST,O SZS 1-12} O E = {(r, 0, 2)Ii Srs 3,0 s E s 2,0 S 25 1 - 2 O E = {(r,...
1. (20 pts) RVs X and Y have joint density function 22 f(x, y) =(0 if O <z<1 and 0<y<2 īf 0 < x < 1 and 0 < y < 2 otherwise (a) Find E(X), V(X), E(Y), and V(Y). (b) Find the covariance cov(X,Y) and the associated correlation ρ (c) Find the marginal densities fx and fy. (Be sure to say where they're nonzero.) (d) Find E(X | Y = 1.5). (e) Are X and Y independent? Give two...
1) Let (S): x² + (z – 1)2 = 1. Then (S) can be represented by: a Ob None of the above 2) Let (S) be the surface given by: y = 4–3x2 – 5z2. Then (S) is: a. an elliptic cone around y-axis b. a circular cone around y-axis c. an elliptic paraboloid around y-axis d. a circular paraboloid around y-axis e. an ellipsoid O a. O b. O c. O d. O e.
22) Choose the best Lewis structure for SO42 A) :0-S-O: B) :S- O: C) D) :O-S-O: 23) Draw the Lewis structure for NO2 including any valid resonance structures. Which of the following statements is TRUE? A) The nitrite ion contains one N-O single bond and one N-O double bond B) The nitrite ion contains two N-O bonds that are equivalent to 1 bonds 2 C) The nitrite ion contains two N-O double bonds D) The nitrite ion contains two N-O...
Evaluate ∫∫∫ E √ x 2 + y 2 + z 2 d V where E lies above the cone z = √ x 2 + y 2 and between the spheres x 2 + y 2 + z 2 = 1 and x 2 + y 2 + z 2 = 9 . df (76 KB) 2. Evaluate r2 + y2 + 22 dV x2 + y2 and between the spheres r? + y2 + 2 = 1 and...
14. Let S be the cylinder {(x, y, z)| x2 +22 = 25,0 SY <2}. Orient S by the outward pointing normal n = (x/5,0,2/5). Evaluate Fds, where F(x, y, z) = (x – 2, y, x + 2). Hint: The area of a cylinder of radius r and height h is 2nrh.
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies between the cones z = √x^2 + y^2 and z = √3x^2 + 3y^2. (1) Let S be the part of the sphere x2 + y2 + Z2-4 that lies between the cones X +y and z a) Find a differentiable parametrization of S b) Find the area of S c) Find 22 dS. (1) Let S be the part of the sphere...
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z) 4, V(Y) = 3 Let U X 3Y +Z and W = 2X + Y + Z 1, and Cov(X, Z) = -1 Compute E(U) and V (U) b. Compute Cov(U, W). а.
Obtain E(Z|X), Var(Z|X) and verify that E(E(Z|X)) =E(Z), Var(E(Z|X))+E(Var(Z|X)) =Var(Z) 3. Let X, Y be independent Exponential (1) random variables. Define 1, if X Y<2 Obtain E (Z|X), Var(ZX) and verify that E(E(Zx)) E(Z), Var(E(Z|X))+E(Var(Z|X)) - Var(Z)