In article <[EMAIL PROTECTED]>,
Sloppy Joe <[EMAIL PROTECTED]> wrote:
>Greetings -
>Suppose I have a method such as a fair 6-sided die. I roll the die 10
>times and get the following trial history:
>3-5-1-3-6-4-6-2-1-5
>From what I can recall from probability, I cannot predict the next roll
>of the die based on the previous rolls. Each number on the die will
>have an equal probability of occuring on the 11th roll no matter what
>has occurred previously: 1/6. My question is this ...
>How can this be proven mathematically?
>Thanks for any help!
This follows from independence. The usual, and in
my opinion quite poor, "definition" of independence
(skipping some steps) is the if one has k independent
random variables,
P(X_i \in E_i for all i) = \prod P(X_i \in E_i);
this is enough to get the result you want. A better
"definition" is that if one forms an even A from some
of the variables, the conditional probability of A
given any information about the rest of them is the
same as the unconditional probability; this is the
way it is used, anyhow.
--
This address is for information only. I do not claim that these views
are those of the Statistics Department or of Purdue University.
Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399
[EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
