## 2/15/2013

### One mouse(keyboard) and Two(three) Computers

If you want to handle two or three computer by one mouse and keyboard, this tool is very useful.
The synergy tool supports this work.

The web site is http://synergy-foss.org
The principle is using server and client of TCP/IP.

This tool is freeware and easy to use.
And it also can use on the mac os.

Thank you.

### Covariance matrix example

The definition of covariance is

Cov(x, y) = E[ (X-E(X)) * (Y-E[Y]) ]

where E is abbreviation of expectation. It is same with Mean.
so..
X = [1 2 3 4 5];
E(X) -> 3 or 3.75
3 is the result of "sum(X)/5"
3.75 is the result of "sum(X)/(5-1)"

In the statistics, mean is divided by N-1 to avoid outlier data affection.

*Example of Covariance

X = [ 2 3 4 2 1 4]
Y = [ 2 4 2 1 6 8]

meanX = sum(X) / 6 -> 2.667
(X - meanX) -> [-0.6667    0.3333    1.3333   -0.6667   -1.6667    1.3333]
(X - meanX) * (X -meanX) -> [ 0.4444    0.1111    1.7778    0.4444    2.7778    1.7778]

cov(x, x) -> sum( ( (X - meanX) * (X -meanX) ) ) / (N-1)
-> 1.4667

cov of X, Y is like that
-> cov(x,x)   cov(x,y)
cov(x,y)   cov(y,y)

-> 1.4667  0.5333
0.5333  7.3667

in the matlab...