0
votes
0answers
28 views

Countable Baye's theorem?

Disclaimer: If this is a foolish question, I'm sorry.. this is the first time I've looked at probability theory in very many years, and have begun to re-read everything from scratch... Question: If ...
2
votes
4answers
80 views

How does one explain basic probability theory to a layman?

I have recently been involved in a number of discussions with people with little or no background in mathematics when we considered a problem of the following shape. A random event is going to ...
52
votes
3answers
5k views

Mathematical research of Pokémon

In competitive Pokémon-play, two players pick a team of six Pokémon out of the 718 available. These are picked independently, that is, player $A$ is unaware of player $B$'s choice of Pokémon. Some ...
1
vote
0answers
73 views

How can I learn to think in probability given my background?

I have this question for some time now and I've decided to ask here. I'm a student of Physics and I'm taking a probability course. Currently I'm used to deal with Physics itself (mechanics, ...
3
votes
3answers
46 views

Confusing -Probabilities.!!

Ok so far what i understand is this lets say...Having to draw a card from 52card-deck its probability is of course 1/52.Now the probability to say that i will keep drawing this same card 10 times of ...
1
vote
1answer
36 views

Prerequisites for studying Introduction to probability theory by William Feller,vol 1 & vol 2?

I know calculus, real analysis, discrete mathematics and applied probability, and want to know what else do I need to know to self-study both the probability books by Feller?
5
votes
5answers
112 views

How can probabilities be modeled in a universe where time travel is possible?

Please don't take this as a joke, its actually a serious question. If it sounds silly its only because of my (lack of) understanding of probabilities, but my motivation is genuine. Lets take the ...
7
votes
2answers
539 views

Why does probability change as you change perspective?

I was trying to solve the following question: Out of 2 Boys and 2 Girls, two students are chosen to advance to the next level. What is the probability that two girls advance to the next level ...
0
votes
1answer
23 views

How to call $(E\hat{x} - x)^2$?

Let $\hat{x}$ be an estimation of $x$. Quantity $E(\hat{x} - x)^2$ is called Mean Squared Error. How one would call $(E\hat{x} -x )^2$?
1
vote
1answer
119 views

Real life scenario, probability model required for accidental vs supernatural causation.

A = HUMAN 1 B = HUMAN 2 A is related to B, specifically A is the father of B A goes on holiday 5 years ago, staying in a hotel in popular tourist spot near Scotland (long way from home) During ...
5
votes
2answers
163 views

Why is probability so unintuitive to us? [closed]

There are so many famous paradoxes which are examples of how humans are unable to intuitively understand probability -- there's a discrepancy between their supposed actual experience and the ...
0
votes
2answers
96 views

Intuitive idea behind the probability density function

as an application of Calculus, I am currently teaching some material about continuous random variables. My main example is the height $X$ of a French male chosen randomly in the French population. ...
1
vote
0answers
47 views

Studying probability from a non-measure-theoretic text: how much am I missing?

Recently I took a Master's-level class on probability. I was very interested in the material, but the class itself was average. It used a textbook which I didn't care for (by Grimmett and Stirzaker). ...
3
votes
4answers
56 views

Soft question about Probability on the assumption “could have happened other way”

When a random experiment results in a particular outcome we beleive it could have resulted in some other possible outcome as well. Consider, for example, an experiment of flipping a coin which has ...
1
vote
2answers
53 views

Summations Question

I'm not used to dealing with summations and there's a lot of summation in probability apparently. There's all these tips and technique that the books assume you to know. I'm used to working with ...
1
vote
2answers
148 views

Is there any surprising elementary probability problem that result in surprising solution like the Monty Hall problem?

For recreational purpose, i haven't seen a interesting elemetary probability question quite a while. Is there any surprising elementary probability problem that result in surprising solution like the ...
3
votes
1answer
340 views

Real Analysis and Statistics

What level of real analysis do you think is desirable for the study of statistics? I know that for many statisticians with applied focus, rigorous mathematics tend to give them a headache and I am ...
0
votes
2answers
49 views

Mapping Normal distribution to a new bounded distribution.

My question is vague. I am looking for distributions that can be obtained from Normal distribution by mapping it to a bounded interval. "By mapping" I mean that a probability distribution ...
2
votes
1answer
121 views

Explaining probability theory versus statistics

I'm not sure whether this question was asked before, but it's hard to search because of lots and lots non-descriptive titles like "statistics and probability". The context: There is an anecdote I ...
2
votes
1answer
130 views

Complex Analysis and Probability Theory

My question is a general one. I know that in complex analysis we find some very powerful theorems but given that my main area of study is Statistics and Probability, does complex analysis have ...
8
votes
2answers
192 views

Why do we want probabilities to be *countably* additive?

In probability theory, it is (as far as I am aware) universal to equate "probability" with a probabilistic measure in the sense of measure theory (possibly a particularly well behaved measure, but ...
0
votes
2answers
92 views

Question on meaning probability of coin tosses?

I have a question on the fundamental meaning of probability. The most familiar example of probability, is the probability of $\frac 12$ for $\text{H}$ and $\text{T}$, each for a single toss of an ...
1
vote
2answers
279 views

What combination of even and odd numbers would you prefer for $5$ digit lottery ticket?

I sometimes play lottery. The tickets are $5$ digit numbers, for example $34298$. I always buy a ticket which have $2$ even, $3$ odd numbers on it or vice versa, even though I know that it does not ...
4
votes
2answers
136 views

Intuitive explanation for $\mathbb{E}X= \int_0^\infty 1-F(x) \, dx$

I can see by manipulating the expression why $\mathbb{E}X$ works out to be $\int_0^\infty 1-F(x)\,dx$, where $F$ is the distribution function of $X$, but what is an intuitive explanation for why that ...
4
votes
1answer
61 views

Gaussian density function satisfies $y'=-xy$. Coincidence?

Is part of the rationale for the Gaussian distribution that the density function satisfies the differential equation $y' = -xy$? Or is this more or less incidental?
2
votes
0answers
202 views

The most fundamental papers in stochastic analysis

I have soft a question. What papers will be good to on start and allow me to make little step into research, without harm for reader. I am interested in an stochastic analysis. I am looking for ...
3
votes
0answers
73 views

Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas?

Some long and good prerequisite textbooks to the graduate probability textbook by shiryaev and boas? It seems that it have a big gap between this graduate textbooks and the easier ones.
4
votes
2answers
192 views

Does introducing penalties for getting true/false questions incorrect result in higher skill penetration (less luck/variance)?

A student is asked to answer 50 true/false questions and he would get 35 right and 15 incorrect if he had to put his best guesses for each question down. Now, for each question he has a certain ...
2
votes
0answers
32 views

Expectation of the area [duplicate]

Choose randomly three points in the unit square $D=\{(x,y)\mid 0\leq x, y\leq 1\}$, is it possible to calculate the expectation of the area of the triangle with the three points as vertexes? (Of ...
3
votes
1answer
57 views

Expected Value of Students on a Bus

There's a question in my probability book that says there are $148$ students on $4$ buses containing $40, 33, 25, 50$ students, respectively. If we let $X$ denote the number of students that were on ...
2
votes
2answers
77 views

Conditional events that are not in the event algebra?

The Wikip. page on conditional event algebra states that: David Lewis showed that in orthodox probability theory, only certain trivial Boolean algebras with very few elements contain, for any ...
0
votes
2answers
62 views

Probability of Intersections

I'm studying for an exam tomorrow, and I'm definitely over thinking it. Out of a normal deck of $52$ cards, $2$ cards are taken without replacement. Given two events: $A_c$ and $B$, where $A_c =$ {an ...
1
vote
3answers
6k views

Probability Of Union/Intersection Of Two Events

I understand the rules for finding the probability of A or B occurring. However, the rules of finding the probability of A and B happening are a bit more elusive. In the former you add, which makes ...
4
votes
2answers
280 views

Intuition Of Conditional Probability Equation

I was wondering if any one of you had any intuitive insight regarding the conditional probability equation, $P(A\mid B) = \large \frac{P(A \cap B)}{P(B)}$. In my textbook, they give a mere definition, ...
0
votes
1answer
25 views

How to obtain estimate of covariance matrix that will be guarantee to be semi-positive define?

How to obtain estimate of covariance matrix that will be guarantee to be semi-positive define ? (Is CrossValidated better place for this question ?)
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 ...
-1
votes
1answer
134 views

What does it mean for a random variable to describe an experiment?

I often hear the expression, random variable (or sequence of rd's) to describes an experiment (or sequence of experiments. But that sound totally unrigorous to me: So we're given a mapping $X:\Omega ...
2
votes
2answers
83 views

Probability: assignment vs. measurement

"It is worth emphasizing that probabilities are assigned not measured." -- TJ Loredo "From Laplace to SN1987A" in "Max Entropy and Bayesian Methods" 1990. Is there a logical way to distinguish what ...
2
votes
5answers
229 views

Why do you need to specify that a coin is fair?

This sounds like the kind of etherial question that generally gets dropped from stack exchange sites, but I don't know of a better venue to ask so I'm hoping this question will help other folks with a ...
1
vote
1answer
1k views

What is the best way to compare probabilities?

If you have two different events with different (known) probabilities, what is the best way to compare the probabilities? For example, the relationship between $0.5$ and $0.7$ is not the same as ...
1
vote
1answer
321 views

What is the relationship between variance and energy

I was speaking with someone today who told me that variance, in the sense of probability theory, is equivalent mathematically to energy in physics. Can anyone elaborate on this relationship?
17
votes
1answer
304 views

Understanding what $\sqrt{p}$ means for an event of probability $p$

Say I have a random event $E$ with probability $p$. There is a natural interpretation in terms of $E$ for the probability $p^2$: it's the probability that $E$ occurs twice if I perform two independent ...
3
votes
0answers
87 views

Fixed marginals of joint distribution: status

One of the well-known problems of classical probability theory is the determination of the set of all extreme points in the convex set of all probability distributions in a product Borel space $\left ...
2
votes
1answer
81 views

What is the utility in writing pdfs in terms of their kernel?

Consider the normal distribution. We know that $$p(x| \mu, \sigma^2) = \frac{1}{\sqrt{2 \pi \sigma^{2}}} e^{-\frac{(x-\mu)^{2}}{2 \sigma^{2}}} $$ The kernel is $$ p(x| \mu, \sigma^{2}) \propto ...
0
votes
1answer
180 views

Name of probability distribution

Does this distribution have a name: $f(x) = yx^{y-1}$ for $0 < x<1$ and $y>0$? It looks like an exponential distribution. Or is it a nameless distribution?
3
votes
1answer
332 views

Exponential distribution as limiting distribution

I wonder if there are well-known and studied cases involving Exponential distribution as limiting distribution. I also wonder if this would contradict Central Limit theorem.
1
vote
1answer
73 views

Monty hosting a new show

I imagine the following setup. There is a contestant who has to pick one of three doors. How many prizes will be hidden is determined at random in the following way. Monty will toss a fair coin and ...
4
votes
5answers
419 views

Sleeping Mathematician (Sleeping Beauty)

I came across the following thought experiment, and I would like to understand whether the controversy around it is justified. Imagine an experiment in which a mathematician is put to sleep with some ...
41
votes
5answers
4k views

Chance of meeting in a bar

Two people have to spend exactly 15 consecutive minutes in a bar on a given day, between 12:00 and 13:00. Assuming uniform arrival times, what is the probability they will meet? I am mainly ...
3
votes
2answers
954 views

Grad degree that mainly deals with probability/game theory/optimization?

I'm currently working but am going to take classes as a non-degree student to beef up the math part of my background. I've only taken calc 1-3, ODEs, linear algebra, logic, and decision theory so my ...