# Tagged Questions

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### 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 ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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?
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### 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 ...
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 ...
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### 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 $(E\hat{x} -x )^2$?
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### 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 ...
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### 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 ...
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### 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. ...
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### 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). ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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.
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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, ...
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### 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 ?)
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 ...
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### 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 ...
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?
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### 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.
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### 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 ...
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### 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 ...