Conference rusure::math

    Well, lets compute it !
    
    In paradise you'll find all the good things you can think of.
    Therefore the value of the paradise is equal to positive infinite
    so V(paradise)= +oo
    On the other hand the value of the hell is equal to the negative
    infinite, so V(hell)= -oo
    
    To go to paradise or to hell is a Bernouli event (two valued event)
    therefore, the probability of going to paradise is P(paradise)=1/2
    and to go to hell is P(hell)=1-P(paradise)=1 - 1/2 = 1/2
    or in an equivalent form P(hell) = P(not paradise)
    
    You expectation to go to paradise (or to hell) is the mathematical
    expected value of that event which is:
    
    E(go-no-go-to-paradise-event) = P(paradise)*V(paradise) + P(hell)*V(hell)=
                                  = 1/2 * (+oo) + 1/2 * (-oo) = +oo + -oo
                                  = oo - oo
    
    Gues what ! this operation can not be done. Simply put "we don't know"
    what is happening.
    
    I hope you had fun ! After all, people say mathematicians have no humor
    but to me it is what Pythagoras (my grand grand grand ... father) said:
    
                "Everything is a number"
    George
    
    P.S.  Sorry for not been able to compose the symbol for the "infinite"
          and using to adjusting oo
    
    

    oo = lim K goes to oo.
    -oo= lim -M goes to oo
    
    so oo - oo = lim K + lim -M  = lim (K-M) = lim N
                  oo      oo       oo          oo
    
    if N<0 , Expectation is Hell
    if N>0 , Expectation is halaloya
    if B=0 , lim 0 = 0  , so you go to neither
             oo 
    
    
            
          

    re .1
    
    >To go to paradise or to hell is a Bernouli event (two valued event)
    >therefore, the probability of going to paradise is P(paradise)=1/2
    >and to go to hell is P(hell)=1-P(paradise)=1 - 1/2 = 1/2
    >or in an equivalent form P(hell) = P(not paradise)
    
    This is (or implies) an additional assumption.  Bernoulli events can
    come in all kinds of (probabilistic) flavors including "unspecified",
    
    	P(X) = p,  0 <= p <= 1
    
    The equiprobable case is just a special case.
    
    Dick

RE: .3 (Dick)

    If we go to a Bayesian probability model we can justify a probability
    of 1/2 by the Principle of Prior Ignorance.  (Though we could also
    use a heirarchical Bayesian model and apply the Principle one step
    removed -- which would make E(P(hell)) = E(P(paradise)) = 1/2 rather
    than P(hell) = P(paradise) = 1/2).

				    Topher

.4>    If we go to a Bayesian probability model we can justify a probability
>    of 1/2 by the Principle of Prior Ignorance.  (Though we could also
>    use a heirarchical Bayesian model and apply the Principle one step
>    removed -- which would make E(P(hell)) = E(P(paradise)) = 1/2 rather
>    than P(hell) = P(paradise) = 1/2).

We can use this principle only when we have no knowledge relevant to the
probability in question.  There are many opinions as to relevant knowledge
in this area.

.1>    E(go-no-go-to-paradise-event) = P(paradise)*V(paradise) + P(hell)*V(hell)=
>                                  = 1/2 * (+oo) + 1/2 * (-oo) = +oo + -oo
>                                  = oo - oo

The formula you are using is appropriate to calculating your expected 
reward, not the expectation of an event (a phrase for which I know no meaning).

RE: .5 (Wally)

>We can use this principle only when we have no knowledge relevant to the
>probability in question.  There are many opinions as to relevant knowledge
>in this area.

    We can also apply it if we choose to disregard our prior belief
    (consistant belief rather than knowledge ("justified belief") is at
    issue) which is frequently done in practical application of Bayesian
    belief.  We might do this precisely because of the varying opinions and
    our ignorance as to how to weight those opinions (basically truncating
    a heirarchical Bayesian model).

					Topher

    We can always make a model custom fitted to our mental states.  My
    issue is with artificially limiting ourselves by failing to recognize
    unstated assumptions.
    
    Dick

Just how *does* one pronounce "Bayesian"?

Dan

RE: .8 (Dan)

    Either bays-Ian or bayzh-Ian, where zh is the phoneme (relatively rare
    in English) found in the words "azure" and "confusion."  I've heard
    it both ways.  The first is probably the "purer" since it corresponds
    to the pronunciation of the name Bayes (bays), the second is what I
    seem to use most often.

					Topher

    I've taught hundreds of kids to use:  bay-EEE-zh-yan
    
    Where "EEE-zh" is the same sound one makes after tasting sauce made
    from overripe cranberries.
    
    Don't worry if it's the wrong pronunciation, most of my students have
    long forgotten it anyway...
    
      John