Homework Answers
T has cumulative distribution function F(t) = 1-(2/t)?, t> 2 otherwise Let Y = T2 and...
T has cumulative distribution function F(t) = 1-(2/t)?, t> 2 otherwise Let Y = T2 and let g(y) be the pdf of Y. Find g(y) for y> 4. A. 8/43 B.8/43/2 c. 4/y? D. 16/y E. 1024/y: Reset Selection
4. Let f(x, y) = 6x, x > 0, y > 0, x +y < 1....
4. Let f(x, y) = 6x, x > 0, y > 0, x +y < 1. Find P(X< }). (a) .3827 (b) .2593 (c).2126 (d).1875 (e).1383
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5...
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5 St<20 10, 0<t<5 and t > 20
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the...
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.
>> x = 0; y = 1 >> while y < 40 x = x +...
>> x = 0; y = 1 >> while y < 40 x = x + 1; y = y + 2^x; end >> disp(x), disp(y) 4. >> f = @ (x, y, z) sqrt ((x + y)/z); >> f(6, 12, 2) >> f(20, 16, 1) 5. >> A = [1 2; 1 -2]; >> B = [3; 5]; >> D = det(A) >> C = inv(A) * B
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x...
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...
L UULIOL A (a) Evaluate the conditional distribution K(y/x=1), given the joint probability function f(x,y)= e-*-,x>0,y>0....
L UULIOL A (a) Evaluate the conditional distribution K(y/x=1), given the joint probability function f(x,y)= e-*-,x>0,y>0. 4 (bl ynloin the 1 1 :
NIS 4) The joint pdf of X and Y is 1, 0<x<1, 0<y< 2x, fx,8(8,y) =...
NIS 4) The joint pdf of X and Y is 1, 0<x<1, 0<y< 2x, fx,8(8,y) = { 0, otherwise. otherwise. or 1 (Note: This pdf is positive (having the value 1) on a triangular region in the first quadrant having area 1.) Give the cdf of V = min{X, Y}. x
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For each of the foll...
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For each of the following functions g determine if the corresponding functionf is continuous on the whole plane. Use "T" for true,"F" for false 2. g(x, y) 9x2y 3. gx, y)-4 sin) 4. g(x, y) xy sin(xy) 5. g(x, y) 3xy
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For...
Solve heat equation in a rectangle du = k ( ou + dou), 0<x<t, 0<y< 1,...
Solve heat equation in a rectangle du = k ( ou + dou), 0<x<t, 0<y< 1, t> 0 u(x, 0, 1) = 0, uy(x,1,1) = 0, with boundary conditions u(O, y,t) = 0, u(r, y, t) = 0, and initial condition u(x, y,0) = (y – į v?) sin(2x).
T has cumulative distribution function F(t) = 1-(2/t)?, t> 2 otherwise Let Y = T2 and let g(y) be the pdf of Y. Find g(y) for y> 4. A. 8/43 B.8/43/2 c. 4/y? D. 16/y E. 1024/y: Reset Selection
4. Let f(x, y) = 6x, x > 0, y > 0, x +y < 1. Find P(X< }). (a) .3827 (b) .2593 (c).2126 (d).1875 (e).1383
2y + y + 2y = g(t), (O) = 0, y'(0) = 0 where g) 5 St<20 10, 0<t<5 and t > 20
5. (40 points) Let f(x,y) = (x + y),0 < 2,2 <y < 1 be the joint pdf of X and Y. (1) Find the marginal probability density functions fx(x) and fy(y). (2) Find the means hx and my. (3) Find P(X>01Y > 0.5). (4) Find the correlation coefficient p.
>> x = 0; y = 1 >> while y < 40 x = x + 1; y = y + 2^x; end >> disp(x), disp(y) 4. >> f = @ (x, y, z) sqrt ((x + y)/z); >> f(6, 12, 2) >> f(20, 16, 1) 5. >> A = [1 2; 1 -2]; >> B = [3; 5]; >> D = det(A) >> C = inv(A) * B
(1 point) Find the solution of xy" + 5xy' + (4 + 1x)y = 0, x > 0 of the form Yi = x n=0 where co = 1. Enter r = -2 Cn = - n= 1,2,3,...
L UULIOL A (a) Evaluate the conditional distribution K(y/x=1), given the joint probability function f(x,y)= e-*-,x>0,y>0. 4 (bl ynloin the 1 1 :
NIS 4) The joint pdf of X and Y is 1, 0<x<1, 0<y< 2x, fx,8(8,y) = { 0, otherwise. otherwise. or 1 (Note: This pdf is positive (having the value 1) on a triangular region in the first quadrant having area 1.) Give the cdf of V = min{X, Y}. x
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For each of the following functions g determine if the corresponding functionf is continuous on the whole plane. Use "T" for true,"F" for false 2. g(x, y) 9x2y 3. gx, y)-4 sin) 4. g(x, y) xy sin(xy) 5. g(x, y) 3xy
(1 point) A function f is defined on the whole of the x, y-plane as follows: f(x,y)0 fy0 otherwise For...
Solve heat equation in a rectangle du = k ( ou + dou), 0<x<t, 0<y< 1, t> 0 u(x, 0, 1) = 0, uy(x,1,1) = 0, with boundary conditions u(O, y,t) = 0, u(r, y, t) = 0, and initial condition u(x, y,0) = (y – į v?) sin(2x).
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