[sage-devel] Re: Expected value of probability space

2008-12-01 Thread William Stein
On Sun, Nov 30, 2008 at 9:39 PM, Paul Butler <[EMAIL PROTECTED]> wrote: > I've been experimenting with probability and found that in Sage, a > probability space is also a random variable by inheritance. This may be > useful. Without it, creating a random variable requires two classes: a > probabil

[sage-devel] Re: Expected value of probability space

2008-12-01 Thread William Stein
[Another response in this thread from David Kohel (who maybe should be posting on list)] Hi William and Paul, Actually, I correct myself -- the average should be over the values of the function, weighted by the probabilities. The domain of the function (the keys) can be in any set (e.g. "A","B"

[sage-devel] Re: Expected value of probability space

2008-12-01 Thread Paul Butler
Hi David, Thanks for explaining that, I see how that causes problems when S is not a set of numbers. Even so, would it make sense for the random variable ps to be the identity function X(x) = x on the probability space ps? Currently the random variable ps is the function X(x) = P(x). Is this a use

[sage-devel] Re: Expected value of probability space

2008-12-01 Thread David Kohel
Hi Paul, > Thanks for explaining that, I see how that causes problems when S is not a > set of numbers. Even so, would it make sense for the random variable ps to > be the identity function X(x) = x on the probability space ps? Currently the > random variable ps is the function X(x) = P(x). Is th

[sage-devel] Re: Expected value of probability space

2008-12-01 Thread Paul Butler
Hi David, When I was referring to the "probability space ps" and the "random variable ps", I was referring to the fact that ps is by inheritance a probability space and a random variable (is_DiscreteProbabilitySpace(ps) == is_DiscreteRandomVariable(ps) == True). I do see that the values are neces

[sage-devel] Re: Expected value of probability space

2008-12-02 Thread Robert Dodier
On Dec 1, 1:48 am, "William Stein" <[EMAIL PROTECTED]> wrote: > [Another response in this thread from David Kohel (who maybe should be > posting on list)] > Actually, I correct myself -- the average should be over the values > of the function, weighted by the probabilities. The domain of the >