(a) f'(-3) d (b) f'(-2) y=f(x) (c) f(-1) bn aimil 1 (d) f'(0) 10 1 (e)...
using discrete structures 3. Consider the function F(x, y, z) for x, y, z z 0 defined as follows: a. F(x, y, 0)-y+1 b. F(x, 0, 1)-x c, F(x, 0, 2) = 0 d. F(x, 0, z+ 3)-1 e. F(x, y, z)-F(x, F(x, y-1, z), z-1) Using Induction, prove the following a. F(x, y, 1)-x +y b, F(x, y, 2) = xy c. F(x, y, 3)-xy 3. Consider the function F(x, y, z) for x, y, z z 0 defined...
Problem 6.8. Let X = {1, 2, 3}, Y = {a, b, c, d, e}. (a) Let f : X → Y be a function, given by f(1) = a, f(2) = b, f(3) = c. Prove there exists a function g : Y → X such that g ◦f = id X . Is g the inverse function to f? (Hint: define g on f(X) to make g ◦ f = id X . Then define g on Y...
Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y < (c) Find the marginal pdf of X. (d) Find the conditional pdf of Y given that X = x. (e) Find E[Y IX x (f) Find E[E[YX]]. (g) Find Cov(X, Y) (h) Are X and Y independent? Suppose that f(x, y) = cx, for 0 y x 2. (a) Find c. (b) Find P(x > 1 and Y
2. The joint pmf of X and Y is given below. f(x,y) 0 1 2 Y 0 1/10 3/100 1 3/10 2/10 1/10 a. Compute P(Y = 0|1 < X < 2). b. Compute E(X|Y = y) for y = 0,1. C. Evaluate Ey[E(X|Y)] using the formula Ey [E(X|Y)] = {y E(X|Y = y) f (y) and the results of part (b). d. Evaluate E(X) using the formula E(X) = Exxfx(x). Note that your answers in (c) and (d) should...
a. e. b. f. 7. Given the function f(x) = 4(2)* - 3 , the equation of the horizontal asymptote is a. X=-3 e. y=-3 b. X=4 f. y = -2 c. X= 3 g y = 2 d. y = 0 h. none of these 8. If we apply the mapping (x,y) → (x-3,- 2y + 1) to f(x) = (3)* , the equation of the image is y = 2(3) *-3 + 1 y=-(3)*+2 + 1 =-2(3)*+3+1 y=-2(3)*+3...
1. Decide if the following statements are true or false. Give an explanation for your answer. (a) If 0 < an < bn and Σ an converges, then Σ bn converges (b) If 0 < an < bn and Σ an diverges, then Σ bn diverges. (c) If bn an 0 andbcoverges, then an converges (d) If Σ an converges, then Σ|an| converges (e) If Σ an converges, then linn lan +1/a (f) Σχ00(-1)"cos(nn) is an alternating series (g) The...
Let F (x, y, 2) =zi+xj+yk. Find the divergence of F. a. -2 b. -1 c. 0 d. 1 e. 2 f. 3 g. 4 h. 5
Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that is defined on a region D that contains C and f(x,y) < M for all (x, y) E D. Show that f(x, y)ds 3 Me Hint: Use the following fact from single variable calculus: If f(x) g(x) for a KrS b, then (x)dJ() dr. Problem 2 Suppose C is a curve of length (, and f(x, y) is a continuous function that...
Find the slope of the line: 10 x - 3 y+ 2 = 0 2 a) b) 10 10 c) 3 10 d) e) 10 None of the above. f) 이의 Find the slope of the line: 10 x - 3 y+ 2 = 0 2 a) b) 10 10 c) 3 10 d) e) 10 None of the above. f) 이의
25. The point (0, 0) is the only critical point of the function f(,y)(2+y)++3 in the interior of the disk D +(+1 s 9/4). The following graph is of z .) restricted to the boundary of D, which is parameterized by -cost, y1n t, for 0s t s 2. Find the absolute minimum value of f(x, y) on D. (A) 0 (B) 2 (C) 3 25 3.25 (E) 2.9 (F) 3 (G) 3.25 (H) 4 25.. -8.25 (J) 9.25 3.75...