Total system of events-really need help

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lucky_luke - 30 Oct 2005 13:14 GMT

hi

A set has 2^n subsets. For this reason we can make 2^n
different sums of events ( one of those events is also
impossible event N ) from sample space containing n
elementary events

Out of this events we can pick those in more than just
one way, the sum of which is certain event and the individual two events can't be combined(I'm not shure how this is meant since I could combine them using 'U'). These events constitute a TOTAL SYSTEM OF EVENTS (TSE) of an experiment X

-What is an english phrase for TSE ?

Let an experiment X be a toss of a dice. Write a few
TSEs for this experiment

- A: dice shows odd number, B:shows even number

- A: dice shows 1, B:dice shows prime number, C: dice
shows 4 or 6

but I'm not shure if when asked for TSE I must include
those events ( A and B in first and A,B,C in second case
) in such way that the result is certain event?

What is with this TSE? Does the name describe an event
that is certain( like A U B U C = G), or it just tells
that I can put all the possible outcomes of an experiment
in one or more event sets, even if I don't intend to
combine those events to get certain event?

-To have TSE must I also include impossible event?
If you noticed, I didn't include it in the example above.

thank you

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Paul Sperry - 31 Oct 2005 06:27 GMT

In article
<21490618.1130674522134.JavaMail.jakarta@nitrogen.mathforum.org>,

> hi
>
> A set has 2^n subsets. For this reason we can make 2^n
> different sums of events ( one of those events is also
> impossible event N ) from sample space containing n
> elementary events

I guess "elementary event" = "outcome" and "certain event" = "sample
space".

> Out of this events we can pick those in more than just
> one way, the sum of which is certain event and the individual two events
[quoted text clipped - 3 lines]
>
> -What is an english phrase for TSE ?

I don't think there is one; an "exhaustive and mutually exclusive set
of events" maybe or, more likely, "a partition of the sample space". I
think there is a language problem here. Still guessing, a "TSE" is a
collection of events such that every outcome belongs to one of the
events ("the sum is certain") and no outcome belongs to two of the
events ("can't be combined"?)- see below.

> Let an experiment X be a toss of a dice. Write a few
> TSEs for this experiment.

["Dice" is plural; "die" is singular - don't ask me why.]

G = all possible outcomes = certain event = sample space =
{1, 2, 3, 4, 5, 6}.

> - A: dice shows odd number, B:shows even number

A = {1, 3, 5}; B = {2, 4, 6}. A \/ B = G; A /\ B = empty (that is,
A /\ B is not possible).

> - A: dice shows 1, B:dice shows prime number, C: dice
> shows 4 or 6

A = {1}; B = {2, 3, 5}; C = {4, 6}. A \/ B \/ C = G; A /\ B = A /\ C =
B /\ C = empty.

> but I'm not shure if when asked for TSE I must include
> those events ( A and B in first and A,B,C in second case
> ) in such way that the result is certain event?

I guess so. In other words, it is certain that every outcome belongs to
one of the events.

> What is with this TSE? Does the name describe an event
> that is certain( like A U B U C = G), or it just tells
> that I can put all the possible outcomes of an experiment
> in one or more event sets, even if I don't intend to
> combine those events to get certain event?

As near as I can tell, for a TSE, every outcome must belong to one of
the events but no outcome belongs to two of them. You don't need to
actually combine the events to get the certain event but you could if
you wanted to.

> -To have TSE must I also include impossible event?

I don't think so.

> If you noticed, I didn't include it in the example above.
>
>
> thank you

Signature

Paul Sperry
Columbia, SC (USA)

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lucky_luke - 31 Oct 2005 15:27 GMT

thank you

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Math Forum / Mathematics / Undergraduate Math / October 2005

Total system of events-really need help