\perp sign = independence? (stat inference, notation question)

I am reading Properties of sample variance, and suddenly this notation comes up with no introductory explanation what it means

as in

since and

(when proving that the sample variance is an unbiased estimator of the population variance)

Then the next chapter said 'the sample mean and the sample variance are independent,

(the Y was supposed to be sample mean, ie with a bar on top, but I couldn't find the way how to place the bar in Latex?)

So my guess is that this sign in statistical inference denotes mutual independence, but I'd like to check.

Thanks!

PS found this in Google

http://www.psych.umn.edu/faculty/wal...gs/rodgers.pdf

apparently, (linearly) independent is not the same as orthogonal or uncorrelated. So what exactly does that 'perpendicular' sign denotes?

more on independent rvs- splitting into indep terms

Right. Thanks.

May I ask another - related - question here (not worth a a new thread). From the same proof, to prove that sample variance is an unbiased estimator of the population variance, the author of my study guide uses a 'trick' of splitting the into independent terms (so that's where the question about sign comes from).

It is done as follows:

I hope you can read that - what is the Latex for 'not equal'??

(And after splitting the sample variance original formula into two parts which are independent, he finds the expected value which, after manipulations, is pop'n variance.)

My question is pretty basic - I don't understand the 'splitting' manipulation above, and especially the meaning of the . Is that the sum of all except the ? Then where is the order of the last term of this sum (I mean n-1 at the top)?

thanks!!