# [R] Probability Question

peter dalgaard pdalgd at gmail.com
Wed Dec 28 09:15:03 CET 2011

```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.)
>
> 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
>
> 	[[alternative HTML version deleted]]
>
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