1. Basic Probability Concepts
Def 1.1: The sample space is the set
- What exactly does this mean?
- How is this different from ? The “1-1 correspondence” part makes me think that , where corresponds with the term “element” used in Def 1.1.
Ex: Experiment=tossing 3 fair coins
I think this corresponds with my , at least in the way that I’m thinking about . Perhaps the difference is that I’m thinking that there is only one way to represent the set of all outcomes when, in fact, it could be represented in multiple ways.
, where corresponds with , corresponds with , etc. So all of these are “equivalent” representations of .
If that is the case, then I think that the definition of should be modified.
Def 1.1′: A sample space of an experiment is a set or .
- I added the phrase “an experiment” to specify that a sample space corresponds with a particular experiment”.
- I changed “the sample space/set” to “a sample space/set” since there could be multiple representations
- I wonder if my incorporation of representation is problematic. For example, does my definition now imply that , or does it allow for isomorphisms? Is there any value to viewing them as different? Or should ?How are these different? How are they the same?
I just looked up the definition of sample space in A First Course in Probability (Ross, 2006), and this is what I found:
“This set of all possible outcomes of an experiment is known as the sample space of the experiment and is denoted by ” (p. 24).
This definition corresponds with my .
Ross, S. (2006). A First Course in Probability. (7th ed.) Pearson Education: Upper Saddle River, NJ.