Let X tilda U(0,3) and Y = X^3. Compute P(5 < Y < 12).
Let X ~ N(0,1), and let Y = 2X + 5. Compute P(Y <= 7)?
Supposed both X and Y are independent and distributed according to Geo(0.2). Compute P(min {X,Y} < 4). Hint: if x tilda Geo(P), then Fx (k) = 1 - (1 - p)^k.
Compute the jacobian:
26) Compute the Jacobian: x=u+5 and y= u-v 15
26) Compute the Jacobian: x=u+5 and y= u-v 15
Let X be exponentially distributed with parameter 3. a) Compute P(X > 6 | X > 2). b) Compute E(7e-12x+8+ 5). c) Let Y be independent from X. Suppose the PDF for Y is f(x) = 2x for 0 ≤ x ≤ 1 (and 0 else). Find the PDF of X + Y.
Let u = u(x,y) and x = x(r,9), y = y(r,). ди ди a. Let x = r cos Q, y = r sin p. Find and a2u ar' 29 ar2 b. u = -x x = r sin 29,y = r tan’ 4, P (1,5). Find ou at the point P. де до
2.11. Let x(t) 11(1-3)-u(t-5) and h(t) = e-3t11(1). (a) Compute y(i) - x(t) * h(t)
5. Let X have the uniform distribution U(0, 1), and let the conditional distribution of Y, given X = x, be U(0, x). Find P(X + Y ≥ 1).
4. Let 3 f(x, y, z) = x’yz-xyz3, 4 P(2, -1, 1), u =< 0, > 5 a). Find the gradient of f. b). Evaluate the gradient at the point P. c). Find the rate of change of f at the point of P in the direction of the vector u.
Let X ~Par (2) and Y = ln(X). Compute P(Y > 1).
1. (5 pts.) TRue or FALse: (a) Let R denote a plane region, and (u,u) = (u(x,y), u(x,y)) be a different set of l (b) Let R denote a plane region, and (u, v) - (u(x, y), v(x, y)) be a different set of coordinates for the Cartesian plane. Then for any function F(u, v F(u, u)dudu- F(u(x,y),o(x,y))dxdy coordinates for the Cartesian plane. Then (c) Let R denote a square of sidelength 2 defined by the inequalities |x-1, lul (3y,...