» Suppose that u depends on z and w, while z and w depend on x and y, where both x and y depend o...
1.2. If w =exp(x+y) and x = sin(311) and y = 21cos(-131), find w/ot in two ways, once by plugging in, and once by the chain rule. 3. Show why it is true that, if f(x, y) = implicitly defines y as a function of x. we can compute the derivative dy/dx as the negative of the quotient of f/ox and 51/by. 4. Find the directional derivative of the function f(x.y) = (x+1)* cos(-3)) at the point (0.1) in in...
Given the following truth table, where X, Y, and Z are input and W is output, write the canonical expression and generate gate-level logical circuit (draw the wire diagram). Given the following truth table, where X, Y, and Z are input and W is output, write the canonical expression and generate gate-level logical circuit (draw the wire diagram). 0 01 0 0 100O 0 110 (0
1. (18 pts.) Short answer: a) Given that f (u,v,w,x, y,z) is a real valued function, what dimension is its graph in? What dimension are its level curves in? (2,1,3). b) Given: g(x,y,z)= x? In (xy+z) Find the direction of maximum ascent c) Find I using integration or geometry: I = 6 dx dy. S: 146 d) Describe and/or draw the region: R= P ={(2,0,0)|9=%;05057; p=17}
let u= ln(x) and v=ln(y) w=ln(z) where x,y,z>0 .Write thr following wxpressiins in terms of u,v, and w. a) ln( squareroot x^5)/ y^3z^2) B) ln (squareroot x^3 4squaroot y)
10.3.8 Suppose that Y = E(Y | X) + Z, where X, Y and Z are random variables. (a) Show that E (Z | X) = 0. (b) Show that Cov(E(Y | X), Ζ) = 0. (Hint. Write Z-Y-E(YİX) and use Theo- rems 3.5.2 and 3.5.4.) (c) Suppose that Z is independent of X. Show that this implies that the conditional distribution of Y given X depends on X only through its conditional mean. (Hint: Evaluate the conditional distribution function...
(1 point) х Suppose w 9 y + where у 2 + sin(2t), and z = z X = e e5t, y 2 + cos(7t). as X. dw A) Use the chain rule to find as a function of x, y, z, and t. Do not rewrite x, y, and z in terms of t, and do not rewrite e e5t d dw 5/y(e^5t)+-x/y^2+1/z(2cos(2t))+(-y/3^2)*(-7sin(7t)) dt Note: You may want to use exp() for the exponential function. Your answer should be...
(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.
Suppose you have three events - X, Y, and Z - where X and Y are mutually exclusive, and together X, Y, and Z are collectively exhaustive. Z is not mutually exclusive with respect to either X or Y. Is this possible? If so, draw a Venn Diagram illustrating how it might be possible.
Consider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a, b, c are constants. The prices of good x and y is denoted by pX and pY respectively. The income is denoted by m. Good z is provided by the government free of cost but the quantity of good z provided by the government depends on the consumption of good x and y chosen by the consumer. For example, if in equilibrium, the consumer...
Suppose Y = X^2 + Z^2,where X , Z are both normally distributed, but they are not independent. What is the distribution of Y? Exponential Distribution Normal distribution Chi Square distribution None of the other answers