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.
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 :-)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*exey = 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*eycorr = covxy/(sqrt(varx)*sqrt(vary))
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.