Probability and Statistics

랴연

Hey lads,

So I've started my postgrad studies and theres a class I'm doing, the basics of which involve a lot of statistics/probability.

Now I was never the best at maths and I'm pretty sure I've never learned a lot of the stuff we're getting presented with, that or I've forgotten it all. Its been 4 years since I studied anything before and at least 7 since I studied any maths at all.

Can someone please recommend some books for probability and statistics ? I need to do a serious crash course in them very quickly.

Some of the stuff I'm expected to know is Bayes Theorem and Gaussian distribution for two examples.

Lads your talking to someone who doesn't know what Sigma is for/does.

Like these for example;

F (x) = P[X ≤ x] for −∞ < x < +∞
X(ζ) ≤b <== See that guy beside the X ? I don't know what that is.
μ <== Don't know.

Any help is very much appreciated. Thank you.

littlecat

Hi there, I can't be of help with the books I'm afraid - it's about 8 years since I did stats and probability, and then it was from notes. To be honest my first port of call would be your lecturer. Lecturers assume a basic knowledge, you have to or you'd never get anywhere, but it's quite possible that your classmates' undergrad courses were of varying content. I'd ask for additional help from them or if they could recommend another postgrad or postdoc who could help explain the basics. I gave grinds when I did my postgrad and it's amazing how just phrasing something differently or passing on your own tricks of memorising and understanding things can make a huge difference. All the best with it!

Grudaire

Regardless of whether you're studying Stats or not, you should read this book:




μ = E(X) = Mean of X

To be honest nobody here can teach you stats, for what you've said though look over Random Variables and Probabilty density and distribution functions for a starter

Fremen

How maths-y is the maths? You can study probability at two very different levels. One from a stats point of view, and one from the point of view of measure theory.

If you're doing measure theoretic probability, you will have been introduced to sigma algebras by now. Jacod and Protter's book "probability essentials" is very good for this perspective. If you don't know what a sigma algebra is, ignore this bit.

If you're doing elementary probability, go to your library and look through the probability section. You'll find books with titles like "probability for engineers". Pick out whichever looks easiest for starters. Your calculus is probably rusty (and calculus is crucial in probability since expectations are basically just integrals) so you may need to review differentiation and integration.
From a google search, Basic Probability Theory with Applications by Mario Lefebvre looks good. It begins with a review of basic calculus concepts. As a rule of thumb, any book which does this is probably a good bet. The Springer Undergraduate Mathematics series tend to be fairly accessible too.

Feel free to post back here if you have any trouble.

Grudaire

Surprisingly good, you'd need a proper stats book to get a bit more into it, and for more worked examples. It covers up to linear regression if I remember right!

It's just a good laugh if you have a half grounding in the theory behind stats. It's not hardhitting stuff, and all the points it illustrates come in cartoon form! This is the clearest page google can find:

랴연

Hey lads, sorry for my first post, it wasn't very informative.

What I need to learn about is;

• Sample Space, Events, Definition of Probability
• Borel-Cantelli Lemmas
• Conditional Probability, Independence
• Random Variables
• Expectation, Variance, Correlation
• Joint distributions
• Conditional Expectation and Prediction
• Multivariate Gaussian distribution
• Random sequences and convergence
• Laws of large numbers, Central Limit Theorem

My class is about pattern recognition and I will be using MatLab in the following few weeks.

If anyone has any more book/other recommendations, it'd be very much appreciated.

Thanks again maths guys.

e11e

hey maths guy,

What course are you doing? I'm thinking of doing a postgrad in statistics but you're post has frightened the life out of me!

Fremen

Meh... it always looks scary beforehand. Flip through a recommended text on google books. If you can follow the first chapter, you'll probably do fine. If you can't, try again with another book.

Remember, they'll start you from near scratch, assuming fairly basic knowledge (say, multivariable calculus and matrices). Not everyone will have a stats background, so they'll start slow.

UrbanSea

Hey guys I was just gonna start a thread on probability in relation to a bet I was thinking.
Say for example there are 7 runners and trying to figure out the first two,is that just 7 Chance 2? That gives you 21,but that can't be all the possobilities for first and second,can it?

RoundTower

yes, if you don't have to get the order right. Try listing them and you'll see.