Consider the joint pmf p(x,y) and marginal pmfs p(x) and p(y) for two discrete random variables X and Y as displayedin the table below.Xp(x,y)123p(y)10.1250.06250.18750.1250.5Y20.06250.06250.1250.250.5p(x)0.18750.1250.31250.3751 Are X and Y independent?No, p(x,y) # p(x)p(y) for x = 1, 3 and yO Yes, p(x,y) = p(x)p(y) for x = 1 and yNo, p(x,y) + p(x)p(y) for x = 0, 2, 3 and yNo, p(x,y) + p(x)p(y) for x = 0, 1, 2, 3 and yNo, p(x,y) = p(x)p(y) for x = 0, 1 and yO No, p(x,y) # p(x)p(y) for all pairs of x and yO Yes, p(x.y) = p(x)p(y) for all pairs of x and yO O O

For the given joint distribution, Are X and Y independent?

Answered: Are X and Y independent? O No, p(x,y) #…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Evaluate f (x - y)(y- z) dV for the box B3 with dimension: [4, 9] × [0, 1] × [0, 1]. (Use symbolic notation and fractions where needed.) ]] (x - y) (y – z) dV = B
10
X+y+z+w=6 2x+3y-w=0 -3x+4y+z+2w=4 x+2y-z+w=0 Select one: a. x=1,y=0,z=2,w=3 b. x=0,y=1,z=3,w=2 C. X=2,y=0,z=3,w=1 d. x=1,y0,z=3,w=2
5. Let f(x, y) = P(X =x,Y = y), X = 2,3,4, Y = 1,2,3,4, where P is given by the table below: X = 2 X = 3 X = 4 Y = 1 Y = 2 Y = 3 1/20 2/20 1/20 2/20 1/20 3/20 1/20 2/20 2/20 2/20 1/20 Y = 4 2/20 For problems (a) - (d) below write your work using the correct notation in terms of f (e.g. f(x, y), fy: f,(3), fyp fxp(4) ): (a) Verify that f is a joint probability mass function. (b) Find the marginal distribution for each random variable. Are both random variables independent? (c) Find the mean and variance of each marginal distribution. (d) Find the conditional probability function of Y given X =3. (e) Find E(Y|X = 3) and V(Y|X = 3). (f) Find P(X+Y =5), P(Y >1), and P(X +Y =5|Y > 1).
(2) Consider the claim: (Vx E N)(3 y E R)P(x, y) = (3 y e R)(Vx E N)P(x, y). (2.1) What is the domain of the predicate P(x, y)? (2.2) Give an example of a predicate P(x, y) for which the above claim is true. (2.3) Give an example of a predicate P(x, y) for which the above claim is false.
Let R(s, t) = G(u(s, t), v(s, t)), where G, u, and v are differentiable, and the following applies. u(-9, 5) = -2 v(-9, 5) Vs(-9, 5) V(-9, 5) G,(-2, 3) : 3 Us(-9, 5) = 6 -4 = -1 = 4 G,(-2, 3) (s '6–)'n = -6 = -7 Find R,(-9, 5) and R,(-9, 5). R(-9, 5) R;(-9, 5) Need Heln? Read It
Let W(s, t) = F(u(s, t), v(s, t)), where F, u, and v are differentiable, and the following applies. u(3,-2) = -6 us(3,-2) = 4 u(3,-2) = -7 Fu(-6, -4) = 0 v(3,-2) = -4 Vs(3,-2) = 9 v(3,-2) = 1 F(-6, -4) = 7 Find We(3,-2) and We(3,-2). Ws(3,-2) = W+(3,-2) =
1. Let f(x, y) =x+2y. Find f(0, 1), f (2, –1), f(a, a), and f(a + h, b) – f(a, b). 2. Let f(x, y) = xy². Find the respective values of f (0, 1), f(-1,2), f(104, 10-2), f (a, a), f(a+h, b), and f(a, b+ k) – f (a, b). %3D 3. Let f(x, y) = 3x² – 2xy+ y. Find f(1, 1), f(-2, 3), ƒ(1/x, 1/y), p = [f(x+h,y) – f(x, y)]/h, and q = [f(x, y + k) – f(x, y)]/k. %3D SECTION 11.2 / PARTIAL DERIVATIVES WITH TWO VARIABLES 411 4. Let f(x, y) = x² + 2xy + y². (a) Find f(-1,2), f(a, a), and f (a + h, b) – f(a, b). (b) Prove that f(2x, 2y) = 2f(x, y), and that f(tx, ty) = tf(x, y) for all t.
|x² + y², x² + y² < 4, y 2 0 0, fxx(x,y) = otherwise
7.) Evaluate F dř. C F(x, y, z) = (3x, 4y, xz) r(t) = (6t+2, 8t - 3,7t), 0≤ t ≤ 1
Evaluate ∫∫∫B2xy2dV
Find fy and f and evaluate each at the given point. Fx, y, 2) = x*y> + 2xyz - syz, (-2, 1, 2) (X, Y, 2) = f(x, y, z) - x, y, 2) - (-2, 1, 2) - -2, 1, 2) = 4-2, 1, 2) = %3D

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