sample space and observational units In stat courses the concept of observational unit is fundamental. When sampling from a population, each element in the sample is called an observational unit (sometimes referred to as an individual). So a sample of size 10 contains 10 observational units (even it the sampling is done with replacement). Each observational unit can have various attributes or variables associated with it. For example, sampling a bunch of cpus from a cpu manufacturing process, each cpu has a clock speed, a physical length, a weight, etc. Sometimes the sample space for this experiment is written as the set of possible weights, or the set of possible lengths, etc. However it seems more accurate to say that the sample space is the set of observational units and that each of the aforementioned variables are random variables which map from the set of observational units to that particular variable's values.
I am stuck however and I don't see how to carry this framework over to an experiment of rolling a single die, or tossing two coins. For example, what are the observational units when I toss two coins? Shouldn't there be 4 of them so that I can get a sample space with the same cardinality as {HH, HT, TH, TT}? Any pointers on this would be appreciated.
 A: For the CPU example, the sample space is composed of all possible draws of a cpu. Each CPU has some probability of being drawn, which may not be uniform. For example, let $\omega_i$ represent drawing CPU $i$, then our sample space $\Omega$ can be represented as $\{ \omega_1,\omega_2,...,\omega_n\}$ and we can say $P(\omega_i)=p_i$ is the probability of drawing that CPU. Now, as you said, we have a number of random variables $W(\omega), S(\omega), L(\omega)$ etc. that map these units to numbers. What we are doing is mapping the "fundamental" outcome (drawing a cpu) with a derived outcome (measured weight, length, etc). Note there that the actual randomness comes from the sampling process, not the cpus themselves (which supposedly have fixed weights, lengths, etc).
Contrast this with the coin and die examples. Here, the randomness is inherent in the object itself, so our sampling process is not over objects but observations or outcomes of a single object. Hence, the equivalent of, say, the (deterministic) length of a randomly chosen cpu is the actual observed value of the die or coin. 
Fundamentally, both sample spaces focus on the random elements of an experiment (cpu's or coins/die values), but that doesn't always imply the sample space consists of different objects. A single object can supply all outcomes for a sample space. As an aside, we could model the cpu experiment as repeated observations of a single cpu that has random length, weight, speed. In this case it would be an exact analog to a die or coin. Mathematically, they are equivalent, but physically, one is wrong.
