Correct me if anything I say is wrong, because that's where I'm having issues... I'm not sure.
Text defines a sample point as one outcome from an experiment. As in, if you flip 4 coins, one sample point is H, H, T, T.
Text then goes on to use the term "elements" to refer to different numbers, without defining its use of the word "element".
Text then goes on to define a "variable" as a numerical interpretation of a sample point. For example, a sample point for 5 people ranking a wine out of 10 could be: [0, 5, 3, 4, 9]. The variable may be defined as the mean of that sample (average of the scores).
Is this all correct?
Element: Is an element a component of a sample point? As in, if your sample point is the result of 4 coins being flipped (H, H, T, T), is one element one coin result (as in, there's 4 elements in the aforementioned sample point)? What is an "element".
Sample Point: The text defined a sample point as the lowest level of breaking down the result of an experiment. It started by giving H or T as an example of sample points. Am I correct in saying a sample point is not based on each individual component, but what you consider to be one measured result in an experiment?
Variable: This is an interpretation of sample points, right?
Combinations Rule (no permutations): This rule was described by the textbook as taking a sample of 'n' elements, from 'N' elements. So if you had a lottery with 54 possible numbers, and a sample size definition of 1, then there's 54 possible outcomes (54 different 1-number lottery ticket possibilities). If your sample size were 2, it would be much greater, since there's more than 54 possible combinations of 2 numbers out of 54. If you define a sample size as 54 numbers, then there's only 1 possible outcome (there'd be 54 possible outcomes, and you'd select all of them in one go, so only 1 outcome).
But I think it would be better described as (Sample Space based on how many elements 'n', a sample point, is chosen to contain) = ((total number of elements)! / ((desired sample point size)! * (total number of elements - desired sample point size)!)
This post was edited by Canadian_Man on Feb 18 2017 01:24am