1
vote
3answers
79 views

Why Maximize Expected Value?

In many instances I've come across (in Game Theory, etc), when trying to choose an optimal strategy it has the criterion that it wants to maximize expected value much of the time. To simplify this ...
3
votes
2answers
137 views

Do the Kolmogorov's axioms permit speaking of frequencies of occurence in any meaningful sense?

It is frequently stated (in textbooks, on Wikipedia) that the "Law of large numbers" in mathematical probability theory is a statement about relative frequencies of occurrence of an event in a finite ...
3
votes
6answers
187 views

Logical issues with the weak law of large numbers and its interpretation

In several probability textbooks I have found what amounts to the following argument: Let A be an event in some probabilistic experiment. Let p=P(A) be the probability of this event occurring in ...
113
votes
23answers
10k views

Can a coin with an unknown bias be treated as fair?

This morning, I wanted to flip a coin to make a decision but no coins were in reach. There was however an SD card on my desk: Given that I don't know the bias of this SD card, would flipping it be ...
1
vote
1answer
62 views

In an infinity of choices, is it possible to guess the correct one?

So I've been thinking about the infinite universes model, where each possible action or event creates a new universe for each outcome. For example, if you flip a coin there will be one universe in ...
2
votes
1answer
122 views

Why Is It Rational to Bet on the Most Probable Event?!

Suppose that someone is going to bet in a game. A dice is rolled, and there are only these two options for betting: Option 1. Give 1 dollar and bet on 6. Option 2. Give 1 dollar and bet on 1, 2, 3, ...
5
votes
1answer
215 views

Is there an introduction to probability and statistics that balances frequentist and bayesian views?

Perhaps, roughly, I might be described as advanced undergraduate regarding mathematics. However, I have not learned statistics and have only learned elementary probability. Does there exist a book or ...
6
votes
1answer
280 views

Age of Stochasticity?

Today I came across D. Mumford's 1999 article The Dawning of the Age of Stochasticity, which is quite remarkable even after more than a decade. The title already indicates the theme, but I copy the ...
8
votes
5answers
537 views

Successful approaches to the modelization of ''randomness''

If you pick a number $x$ randomly from $[0,100]$, we would naturally say that the probability of $x>50$ is $1/2$, right? This is because we assumed that randomly meant that the experiment was to ...
3
votes
4answers
278 views

Why $\sqrt{\frac {\sum(x-\mu)^2} {N}}$ instead of $\frac {\sum{\Bigl|x-\mu\Bigr|}} {N}$? [duplicate]

Possible Duplicate: Motivation behind standard deviation? In statistics very often you see something of the sort: $$ \textrm{quantity}=\sqrt{\frac {\sum(x-\mu)^2} {N}} $$ to measure things ...
6
votes
4answers
285 views

Is probability objective?

As we know, probability is a measure of events. However, is it an objectively attribute of events, or just an illusion in ones' mind? For example, suppose that there is an empty black box with an ...
3
votes
1answer
311 views

Probability and Axiom of Choice

I'm not a logician, so I apologize if what follows translates to nonsense. I would like to try to define a different theory of random choice. I hesitate to call it probability theory because I do not ...
2
votes
4answers
355 views

Evidence of Absence = Absence of Evidence?

Any clever-cloggs out there who can explain the formula below in more simple English please? - Do you agree with the formula?