# [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

```