Write vectors in R2 as (x,y). Define the relation on R2 by
writing (x1,y1) ∼ (x2,y2)...
Write vectors in R2 as (x,y). Define the relation on R2 by
writing (x1,y1) ∼ (x2,y2) iff y1 − sin x1 = y2 − sin x2 . Prove
that ∼ is an equivalence relation.
Find the classes [(0, 0)], [(2, π/2)] and draw them on the
plane. Describe the sets which are the equivalence classes for this
relation.
Define a Q-sequence recursively as
follows.
B.
x, 4 − x is a Q-sequence for any...
Define a Q-sequence recursively as
follows.
B.
x, 4 − x is a Q-sequence for any real number x.
R.
If x1, x2, ,
xj and y1, y2, ,
yk are Q-sequences, so is
x1 − 1,
x2, , xj, y1,
y2, , yk − 3.
Use structural induction (i.e., induction on the recursive
definition) to prove that the sum of the numbers in any
Q-sequence is 4.
Base Case: Any Q-sequence formed by the base
case of the definition has sum
x +...
1. Let x ∼ Np(µ, Σ).
(1) Find the distribution of xp conditional on x1, ....
1. Let x ∼ Np(µ, Σ).
(1) Find the distribution of xp conditional on x1, . . . ,
xp−1.
(2) Suppose Σ =(1 ρ ρ 1 )and let y1 = x1 + x2 and y2 = −x1 + x2.
Determine
the joint distribution of y1 and y2.
(3) Suppose Σ =( σ11 σ12 σ21 σ22 )and define y1 and y2 as in part
(2).Determine the joint distribution of y1 and y2.
Determine the conditional distribution y2 given y1.
Write a complete C program that prompts the user for the
coordinates of two 3- D...
Write a complete C program that prompts the user for the
coordinates of two 3- D points ( x1 , y1 , z1 ) and ( x2 , y2 , z2
) and displays the distance between them computed using the
following formula:
distance= square root of
(x1-x2)2+(y1-y2)2+(z1-z2)2
N particles can move in plane (x,y).
Write down coordinates and momenta of all particles forming...
N particles can move in plane (x,y).
Write down coordinates and momenta of all particles forming the
phase space and determine number of degrees of freedom
s.
(a) x1, px1,
y1, py1,
x2, px2,
y2, py2,…,
xN, pxN,
yN, pyN ,
s=2N
(b) x1, px1,
x2, px2, …,
xN, pxN ,
s=2N
(c) y1, py1,
y2, py2,…,
yN, pyN ,
s=2N
(d) x1, y1,
x2, y2, …,
xN, yN ,
s=2N
and why you choose
1.suppose that Y1 and Y2 are independent random variables
2.suppose that Y1 and Y2each have a...
1.suppose that Y1 and Y2 are independent random variables
2.suppose that Y1 and Y2each have a mean of A and a variance of
B
3.suppose X1 and X2 are related to Y1 and Y2 in the following
way:
X1=C/D x Y1
X2= CY1+DY2
4.suppose A, B, C, and D are constants
What is the expected value of X1?
What is the expected value of X2?
What is the variance of X1?
1.suppose that Y1 and Y2 are independent random variables
2.suppose that Y1 and Y2each have a...
1.suppose that Y1 and Y2 are independent random variables
2.suppose that Y1 and Y2each have a mean of A and a variance of
B
3.suppose X1 and X2 are related to Y1 and Y2 in the following
way:
X1=C/D x Y1
X2= CY1+CY2
4.suppose A, B, C, and D are constants
What is the expected value of the expected value of X1 given
X2{E [E (X1 | X2)]}?
What is the expected value of the expected value of X2 given...
I am not sure what I am doing wrong in this coding. I keep
getting this...
I am not sure what I am doing wrong in this coding. I keep
getting this error. I tried to change it to Circle2D.java but it
still comes an error:
Compiler error: class Circle2D is public, should be
declared in a file named Circle2D.java
public class Circle2D {
public class Exercise10_11 {
public static void main(String[] args) {
Circle2D c1 = new Circle2D(2, 2, 5.5);
System.out.println("area: " +
c1.getArea());
System.out.println("perimeter: " +
c1.getPerimeter());
System.out.println("contains(3, 3): "...