I was looking at the following statement and felt I needed some help in sorting it out:
A random sample of size n from a population $f(x)$ is a collection of n independent random variables $X_1,...,X_n$, each having the distribution $f(x)$.
let us apply the above statement to all freshmen at a certain university where we are interested in their heights and weights, So I guess:
- $f(x)$ would be the population of freshmen at a certain university.
- What exactly does $x$ signify in $f(x)$
- so $X_1,...,X_n$ would be the weight measured for a sample of size $n$ ?
- so for heights would be need $Y_1,...,Y_n$?
- strictly speaking can we use $X$ for both height and weight (I guess no -- it would be meaningless as we're mixing types)?
- The last part of the statement "each having the distribution $f(x)$" has me a bit on tender ground -- would be interested in getting clarifications about that.
Note: The statement above is from: "Statistical Concepts and Methods (Wiley Series in Probability and Statistics), Gouri K. Bhattacharyya, Richard A. Johnson", page 208.