R help - Dec 2011 - Probability Question

Hello,

This is a question from a class I'm not in (it's also winter break).
But,
all the same, I don't know where to start in R with this. It's supposed
to
be done in R.  So, can anyone direct me with a helpful hint or 2, on how to
get started with the question listed below, or tell me how I can re-post
this to Usenet groups sci.stat.consult., so they can help with this
question:

Exercise 1. Let Ω = {H,T,E}(a set with 3 elements, called H ,T and E . You
can think of “heads”, “tails” and “edge” if you like, but this
interpretation is not necessary).

1. List the elements of the powerset P (Ω) of Ω. (Recall that the powerset
of a set is the set of all subsets of that set, including Ø (the empty set)
and the whole set.)

2. Suppose P is a set function on Ω (that is, a rule assigning real numbers
to subsets of Ω). Suppose that

P({H,T}) = 3, P({H,E}) = 3, P({H}) = 1 444

Why is it impossible that P is a probability measure ? (That is, no matter
how P is defined on the remaining subsets of Ω, it can’t be a probability
measure.)
-- 
Best,
Matilda Gogos
matildaelizabethv@gmail.com

	[[alternative HTML version deleted]]

On Dec 28, 2011, at 05:11 , Matilda E. Gogos wrote:
> Hello,
> 
> This is a question from a class I'm not in (it's also winter
break). But,
> all the same, I don't know where to start in R with this. It's
supposed to
> be done in R.  So, can anyone direct me with a helpful hint or 2, on how to
> get started with the question listed below, or tell me how I can re-post
> this to Usenet groups sci.stat.consult., so they can help with this
> question:
We're not supposed to help with homework here, and neither is
sci.stat.consult. However, since it is Christmas...

This looks like a pen-and-paper (theory) exercise, not an R one. Are you sure
that the R requirement is not intended to apply to exercises further down the
list?  You might use expand.grid() to find the elements of the powerset, but
I'm not sure that actually helps understanding.
> 
> Exercise 1. Let ? = {H,T,E}(a set with 3 elements, called H ,T and E . You
> can think of ?heads?, ?tails? and ?edge? if you like, but this
> interpretation is not necessary).
> 
> 1. List the elements of the powerset P (?) of ?. (Recall that the powerset
> of a set is the set of all subsets of that set, including ? (the empty set)
> and the whole set.)
> 
> 2. Suppose P is a set function on ? (that is, a rule assigning real numbers
> to subsets of ?). Suppose that
> 
> P({H,T}) = 3, P({H,E}) = 3, P({H}) = 1 444
> 
> Why is it impossible that P is a probability measure ? (That is, no matter
> how P is defined on the remaining subsets of ?, it can?t be a probability
> measure.)
> -- 
> Best,
> Matilda Gogos
> matildaelizabethv at gmail.com
> 
> 	[[alternative HTML version deleted]]
> 
> ______________________________________________
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> PLEASE do read the posting guide
http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com