Cluster Identification in Graphs definitions

Hello,

I'm reading a paper which can be found at http://www.kyb.tue.mpg.de/fileadmin/user_upload/files/publications/attachments/ClusterIdentificationTR_4587[0].pdf (You'll have to copy paste as the .pdf part doesnt want to link). I'm having difficulty finding the definition of one of the acronyms.

The last complete sentence on the first page says "We always assume that we are given $\displaystyle n$ data points $\displaystyle X_1, ... ,X_n$ which have been drawn i.i.d. from some underlying density on $\displaystyle \mathbb{R}^d$." What does "i.i.d." stand for? and what does it mean? I'm guessing it's a statistical term basically meaning something like "randomly drawn" (or at least that's one of the implications).

Also, when they say "from some underlying density on $\displaystyle \mathbb{R}^d$", I just want to confirm that they are talking about a probability density function $\displaystyle f(x)$ with $\displaystyle x \in \mathbb{R}^d$. Is that correct?

Re: Cluster Identification in Graphs definitions