[...]
>
>[...]
>
>BH>B&T's statement: "In a random situation, options are unlimited
>>and each option is equally probable."
>
>[...]
>
>>SJ>There is nothing wrong with this definition. It is *exactly* what
>>"random" means:
>>
>>"...A random sample is one that allows for equal probability that
>>each elementary unit will be chosen...Random numbers are digits
>>generated by a process which allows for equal probability that each
>>possible number will be the next." (Lapin L., "Statistics for
>>Modern Business Decisions", 1973, pp194-195)
>
>BH>I'm curious whether you took a look at the follow-up post that I
>>mentioned above. There you will find that the 6 volume <Encyclopedia
>>of Mathematics> disagrees with <Statistics for Modern Business
>>Decisions>. The equal probability case is a special case.
>
>SJ>No doubt there are other definitions of "random", especially in a .
>"6 volume <Encyclopedia of Mathematics>"! But "equal probability" is
>the core, definition of "random", as can be seen by these separate
>examples:
>
It is true that one would expect a lot of different definitions
of random in something as exhaustive as a 6 volume encyclopedia.
Sure enough, when I searched closely I did find some mention of
the equal probability situation, but only as a special case.
>SJ>"random mating, in population genetics, condition of unrestricted
>mating, such as exists in large natural populations in which,
>theoretically, any male can mate with any female." ("random mating",
>Encyclopaedia Britannica, 1984, viii:416)
>
this is not the same as saying each male mates with any female
with equal probability.
>SJ>"random sampling, in geology, method of sampling any population of
>values in such a way that any particular value has an equal chance of
>being selected" ("random sampling", Encyclopaedia Britannica, 1984,
>viii:416)
>
>SJ>"random walk, stochastic process based on the problem of
>determining the probable location of a point subject to random
>motions given the probabilities (the same at each step) of moving
>some distance in some direction." ("random walk", Encyclopaedia
>Britannica, 1984, viii:416)
>
I looked this one up in the encyclopedia of mathematics. Saying
that the probabilities are the same at each step doesn't mean
they are equal, only that the probability distribution (whatever
it is) doesn't change from step to step. Again, they say specifically
that random walks with equal probabiliites is a special case.
>BH>They give a very good example (also used by Yockey
>>and by myself in another thread) of tossing a pair of fair die
>>and recording the sum. Surely you would agree that this is a
>>"random situation". Work it out and you will see that the variious
>>random events do not all occur with equal probability.
>
>SJ>Brian switches from "random" in an abstract ideal defintional sense
>to "random" as a "real world" example of the outcome of "tossing a
>pair of fair die". First, there is no such thing "in the real world"
>as "a pair of" perfectly "fair die". Second, even if there was a "a
>pair of fair die", in a small number of tosses, the result would
>not be expected to show "equal probability". But the larger the
>number of tosses, the closer the results would approach "equal
>probability".
>
First of all, the example was used to illustrate the definition
of a "random event".
Secondly, you have it backwards in the above. Assuming the dice
were fair one might observe something close to equal occurence
after a few trials. The larger the number of tosses, the closer
the observed frequencies will coincide with the theoretical
probability distribution. [hint, its more likely you will
roll a 7 than a 2.]
[...]
Brian Harper
Associate Professor
Applied Mechanics
The Ohio State University
"Should I refuse a good dinner simply because I
do not understand the process of digestion?"
-- Oliver Heaviside