Some Notes Pertaining to Ch. 3 of E&T
E&T's use of upper-case and lower-case Roman letters for observed data values and population
values is perhaps nonstandard. Many use X to denote a random variable, and x
to denote the value it assumes. While E&T use lower-case letters to denote observed values,
they use upper-case letters to denote population values. Thus
x7 maybe to be equal to
X9 --- this will occur if the 7th unit selected is the 9th unit of the
population. (In E&T,
x7
is not the observed value of
X7 --- E&T do not use
X7 to denote a random variable.) It can be seen on pages 21 and 25 that E&T use
x to denote a random variable --- so, in E&T, without a subscript a lower-case x is
a random variable, and with a subscript it's an observed value. (Notes: (1) I'll discuss all of this in
class, but really I don't think it's important. (2) I intend to continue to use my convention of
letting
X7 denote a random variable, and
x7 denote the value which it assumes.)
I do not like the sentence that begins on the last line of p. 19. Since the population mean clearly lies
in the interval given (see the last paragraph of Sec. 3.2 on p. 20), it's silly to state that there is about a 68%
chance that it does!
Many would call the frequencies of (3.2) and (3.5) on p. 22 of E&T probabilities instead.
Also note that on p. 22 E&T state that F will not always denote a cdf --- we can think of F
as denoting the underlying distribution of a set of observations, but it need not denote the cdf. (This is
really not too much different from what a lot of people do.)
Note: I intend to spend only a relatively short amount of time discussing the material of Ch. 3 of E&T.
You should be familar with the probability results which are given (even though E&T's use of notation
may seem odd at times).