

1. Let B-(0, 1). Define x + y max(x, y) and x . y-min(x, y), and let the complement of x of be 1-x (ordinary subtraction). Show whether or not B forms a Boolean algebra under these operations. 2. Let S-(0,1 R, and T = { y : 2 < y < 12). Find a one to one correspondence (the actual function) between S and T showing they have the same cardinality. (hint: look at straight lines in the xy-plane)...
When the graph of y=2^x is reflected in the x-axis, and then translated 5 units left and 1 unit down, the equation representing the new graph is:a) y=2^(-x+5)-1b) y=2^(x+5)-1c) y=2^(x-5)+1d) y=2^(x+5)-1
f(x,y) = K(x^2 + y^2) in 0 < x < 1, 0 < y < 1 Determine the value of the constant that makes a joint density function. (a) Find fx(X) (b) Find fy(Y) (a) Find E(X) (b) FindE(Y) (a) Find V(X) (b) Find V(Y) Find the covariance cov(X,Y) Interpret your result.
Suppose X andY have joint density f(x,y)=6*x*y^2 for 0<x<1, 0<y<1. (a) What is P(X+Y ≤1)? (b) Compute the marginal densities fX , fY of X, Y .
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
1. Given that y, - e is a solution of (2x-x') y" +(x-2) y'+2(1-x) y. a. Find the general solution on the interval (2, o). y(3)-1 b. Find a solution of the DE satisfying ¡y(3):0
Find the upward flux of F vector=<x,y,z> across: a.
x^2+y^2+z^2=1, z0
and b. z=1-x^2-y^2, z0.
Please be detail thanks.
We were unable to transcribe this imageWe were unable to transcribe this imageZ S FIND THE UPWARD FLUX OF SX,Y,Z) ACROSS: a. pol + y2 + z = 1, z>0 AND b. ž= 1-x2-, z>O
Question #2 Prove the entropy chain rules a) b) H(X, Y) = H(X|Y) + H(Y) 1(X: Y) = H(X)-H(XIY )
Solve the following:
1. x*y'-2*y-2*x^2*y 2. y xty/(x-5) 3. y'y/x, y(1)-2 4. yy+2*exp(2*x), y(0)=3 5. (1+x)*y+ysin(x), y(-pi/2)=0
1. x*y'-2*y-2*x^2*y 2. y xty/(x-5) 3. y'y/x, y(1)-2 4. yy+2*exp(2*x), y(0)=3 5. (1+x)*y+ysin(x), y(-pi/2)=0
1. (1.5 points) Sketch the following vector fields: (B) B(x,y)=(z-y,2). (C) Vf where f(x,y) = xy
1. (1.5 points) Sketch the following vector fields: (B) B(x,y)=(z-y,2). (C) Vf where f(x,y) = xy
Find the upward flux of F vector=<x,y,z> across: a.
x^2+y^2+z^2=1, z0
and b. z=1-x^2-y^2, z0.
Please be detail thanks.
We were unable to transcribe this imageWe were unable to transcribe this imageZ S FIND THE UPWARD FLUX OF SX,Y,Z) ACROSS: a. pol + y2 + z = 1, z>0 AND b. ž= 1-x2-, z>O