## Monday, April 11, 2005

### Mathematics Mathematics .....

So what is a Radom Variable, Probability distribution dunction , Cumulative distribution function,
markov models.

Computer scientists ususally are supposed to be good in mathematics but that seems not to be the case these days, we see math in the papers and then we want to avoid it as much as possible :) although i am writing this too I do the same :) even though i like math

A genuine effor now to understand the mathematics behind the papers. I started off the day with reading about the paper of data acquisition in sensor networks...

Basic Math behind the paper

Random Variable: A function that maps events to numbers, sounds cool ...

$X(\omega) = \begin{cases}0,& \omega = \texttt{H},\\1,& \omega = \texttt{T}.\end{cases}$
Is an example of a random varibale where H and T represents Heads and Tails respectively. A radom varibale is also defined as a measurable function from a probablity space to a measurable space.
In learning this deinition this introduces some more few new concepts.

Distribution Functions:
Recording all these probabilities of output ranges of a real-valued random variable X yields the probability distribution of X.

I seem to be get these things but somehow somethings seems to lag :) ,
for more references
http://en.wikipedia.org/wiki/Probability_distribution

More on this later ...

Normal Distributions
-----------------------
A very important class of staistical distributions , bell shaped density functions with a single curve. Speaking of it mathematically it needs two quantities which are two quantities have to be specified: the mean , where the peak of the density occurs, and the standard deviation , which indicates the spread or girth of the bell curve

http://www-stat.stanford.edu/~naras/jsm/NormalDensity/NormalDensity.html

Standard deviation determines the shape of the curve , mean determines the shift of the curve.
Covarinace matrix ..............

-Kalyan