## Thursday, July 28, 2011

Follow these instructions to boot into single user mode and change the password of root on Debian.

1) When GRUB loads press 'e'
2) Find the line with initrd and goto the end and add init=/bin/sh
3) Press Ctrl + x to boot
4) You will get a prompt with #
5) You need to remount the root filesystem in read write mode by using the command mount -o remount rw /
6) use the command passwd to set the new password.

Done!

## Saturday, July 9, 2011

### Statistics is FUN!

This summer I am taking a basic statistics course and auditing an advanced one. If the basic one is increasing my knowledge and giving me the confidence the advanced one is killing me!(in a very very good way!) After a very long time have I have had to spend nights understanding things from various textbooks and the joy in doing it is awesome! I am writing this post to share few thoughts and resources related to the topic.

1) In the past many of my friends have asked me for soft copies of ebooks. I download most of them from the following site: http://library.nu
I found almost 90% of the textbooks & novels I searched for from this website. I am using the following four statistics books to keep myself busy! Each book uses a different notation which gets to me more often than not but as of now the patience is paying off.
a) Probability & Statistics by Athanasios Paupoulis
b) Probability & Statistics in Engineering by Hines et. al.
c) Theory and problems of probability & statistics by Schaum series
d) All of statistics by Weisserman

2) I hate calculating expecation, covariance and correlation and all that crap for discrete distributions. Firstly, the calculations are cumbersome and secondly I hate Algebra! So, I put together the following script that calculates these. Just update the pdf and x, y vectors and you will get all the answers you need.

pdf=[11/50, 4/50, 2/50, 1/50, 1/50, 1/50;
8/50, 3/50, 2/50, 1/50, 1/50, 0;
4/50, 3/50, 2/50, 1/50, 0, 0;
3/50, 1/50, 0, 0, 0, 0;
1/50, 0, 0, 0, 0, 0;]
x = [0:5]
y = [0:4]

fx = sum(pdf)
fy = sum(pdf,2)'
ex = sum(x.*fx)
ex2 = sum(x.*x.*fx)
varx = ex2 - ex*ex
ey = sum(y.*fy)
ey2 = sum(y.*y.*fy)
vary = ey2 - ey*ey
[xgrid ygrid] = meshgrid(x,y)
exy = sum(sum(xgrid.*ygrid.*pdf))
covxy = exy - ex*ey
corr = covxy/(sqrt(varx)*sqrt(vary))

3) Proofs have always intrigued me. Although there is lot of fun in using a formula to get the answer and feel satisfied, I always found real satisfaction in deriving the formula. Being a computer science major has deprived me of such opportunities. But thanks to the stats course I get to sit and prove stuff again :-)
I am sharing two of the proofs for which I did not find straightforward solutions online. I hope it helps others who are trying to understand the proofs.