[R] Probability Question

David Winsemius dwinsemius at comcast.net
Wed Dec 28 15:35:54 CET 2011

On Dec 28, 2011, at 3:15 AM, peter dalgaard wrote:

> 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 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.)

I don't think I'm violating the no homework rule too much by pointing  
our that there is a powerset()  function in the sets package. Why one  
wouldn't do this one in their head is a bit beyond me,  but if it's  
really true that these need to be done in R, then maybe the author's  
intent ti to get that package installed and loaded?

>> 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 at gmail.com

David Winsemius, MD
West Hartford, CT

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