Yes. the conditional expectation of X given Y is simply the expectation of X if X and Y are uncorrelated. This is a consequence of one of the properties of conditional expectation.

the statistically independent random variables are uncorrelated but the converse is not true ,i want a counter example,

If I have two source of noise let as say two laser diodes so the pink noise that generate fro both of them is it correlated or uncorrelated

to convert raw data of correlated variables to data matrix of uncorrelated variables (Principal Component)

Yes it is. That is actually true for all random vars, assuming the covariance of the two random vars is zero (they are uncorrelated).

Correlation is a way of testing whether there is a linear relationship between two variables of their transformed versions. If there is no correlation then all that it means is that there is no linear relationship between the two or between their transformed versions. It certainly does not mean that there is no relationship. For example, if y = a*x^2 + b where a and b are constants then, because of symmetry, the correlation between x and y is 0.

In statistics, the Gauss-Markov theorem states that in a linear regression model in which the errors have expectation zero and are uncorrelated and have equal variances, the best linear unbiased estimator (BLUE) of the coefficients is given by the ordinary least squares (OLS) estimator, provided it exists.

In mathematics, "orthogonal" means perpendicular or independent. In linear algebra, vectors are orthogonal if their dot product is zero, indicating they are at right angles to each other. In statistics, orthogonal variables are uncorrelated, making them useful for multi-variable analysis.

(2+2)/(2+2)=1

(2/2)+(2/2)=2

(2*2)-(2/2)=3

(2+2+2)-2=4

(2+2)+(2/2)=5

(2*2*2)-2=6

((2-.2)/.2)+2=7

2+2+2+2=8

(22/2)+2=9

((2+2)*2)+2=10

((2-.2)/.2)+2=11

(2+2+2)*2+=12

(22/2)+2=13

(2/.2)+(2+2)=14

2+(2/2)/.2=15

(2+2)*(2+2)=16

...??????????=17

((2+2)/.2)-2=18

((2+2)-.2)/.2=19

22- √(2+2)=20

230.
2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2*2 = 1073741824

21

As a fraction it is: 2/9

256

2, 128

2, 2, 64

2, 2, 2, 32

2, 2, 2, 2, 16

2, 2, 2, 2, 2, 8

2, 2, 2, 2, 2, 2, 4

2, 2, 2, 2, 2, 2, 2, 2

8192

32

2+2+2+2+2+2+2+2+2+2+2+2+(2x0)

=2+2+2+2+2+2+2+2+2+2+2+2+0

=24

2+2+2=6

2 * 2 * 2 * 2 * 2 * 2 * 2, or 27.

Broken down as follows.....

128

2, 64

2, 2, 32

2, 2, 2, 16

2, 2, 2, 2, 8

2, 2, 2, 2, 2, 4

2, 2, 2, 2, 2, 2, 2

128

2*64

2*2*32

2*2*2*16

2*2*2*2*8

2*2*2*2*2*4

2*2*2*2*2*2*2

2^7

2 + 2 - 2 = 2 or 2+(2-2)=2+0=2

128

2, 64

2, 2, 32

2, 2, 2, 16

2, 2, 2, 2, 8

2, 2, 2, 2, 2, 4

2, 2, 2, 2, 2, 2, 2

2 + 23 = 25

3 + 3 + 19 = 25

3 + 5 + 17 = 25

3 + 11 + 11 = 25

5 + 7 + 13 = 25

7 + 7 + 11 = 25

2 + 2 + 2 + 19 = 25

2 + 2 + 2 + 2 + 17 = 25

2 + 2 + 2 + 2 + 2 + 2 + 13 = 25

2 + 2 + 2 + 2 + 2 + 2 + 2 + 11 = 25

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 7 = 25

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 5 = 25

2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 = 25

800

2, 400

2, 2, 200

2, 2, 2, 100

2, 2, 2, 2, 50

2, 2, 2, 2, 2, 25

2, 2, 2, 2, 2, 5, 5

480

2, 240

2, 2, 120

2, 2, 2, 60

2, 2, 2, 2, 30

2, 2, 2, 2, 2, 15

2, 2, 2, 2, 2, 3, 5

2+2+2+2+2+2+2+2+2+2+2+2

40

Its 4 ;p

-1+(2x9)=17

1 and 9 are not twos.

How about this: (2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2+2) /2 = 17

They are opposite parallel lines with points of (-2, 2) (2, 2) and (-2, -2) (2, -2)

210 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 =1,024
1024

LCM factoring

512=2*2*2*2*2*2*2*2*2

648=2*2*2*2*3*3*3*3

lcm=2*2*2*2*2*2*2*2*2*3*3*3*3=41,472

2

The answer is 0 because at the end it is multiplied by 0

2

Negative numbers do not have prime factorizations.

192

2, 96

2, 2, 48

2, 2, 2, 24

2, 2, 2, 2, 12

2, 2, 2, 2, 2, 6

2, 2, 2, 2, 2, 2, 3

you can break 800 in

2*2*2*2*2*5*5 = 2^5 * 5^2

so its divisible by any combination of multiplying numbers 2,2,2,2,2,5,5 where you can you only one in each combo.

so:

1

2

2*2=4

2*2*2=8

2*2*2*2=16

2*2*2*2*2=32

2*5=10

2*2*5=20

2*2*2*5=40

2*2*2*2*5=80

2*2*2*2*2*5=160

2*5*5=50

2*2*5*5=100

2*2*2*5*5=200

2*2*2*2*5*5=400

2*2*2*2*2*5*5=800

5

5*5=25

2*2*2*2*2*2*2*2*2*2=1024

2^10 = 1024

Gcf

32=2*2*2*2*2

56=2*2*2*7

64=2*2*2*2*2*2

gcf=2*2*2 =8

2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 23 = 23552

1/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/2

1/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/2

1/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/2

1/2 + (11/2)*2 = 1/2 + (3/2)*2 = 1/2 + 3 = 31/2

2*2*2*2*2*2*2*2*2*3

It is: (2+2+2)*2 = 12

(2/2) times (2/2)

(2/2) divided by (2/2)

22 divided by 22

(2 + 2) / (2 + 2)