# Tagged Questions

A probability provides a quantitative description of the likely occurrence of a particular event.

7answers
18k views

### What is the difference between “likelihood” and “probability”?

The wikipedia page claims that likelihood and probability are distinct concepts. In non-technical parlance, "likelihood" is usually a synonym for "probability," but in statistical usage there is a ...
6answers
3k views

### Why does a 95% CI not imply a 95% chance of containing the mean?

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
16answers
6k views

### What's the difference between probability and statistics?

What's the difference between probability and statistics, and why are they studied together?
6answers
2k views

### Motivation for Kolmogorov distance between distributions

There are many ways to measure how similar two probability distributions are. Among methods which are popular (in different circles) are: the Kolmogorov distance: the sup-distance between the ...
3answers
3k views

### A Probability distribution value exceeding 1 is OK?

On the Wikipedia page about naive bayes classifiers here there is this line "P(height|male) = 1.5789 (A probability distribution over 1 is OK. It is the area under the bell curve that is equal to 1.)" ...
12answers
1k views

### The Monty Hall Problem - where does our intuition fail us?

From Wikipedia : Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, ...
7answers
1k views

### What is the probability that this person is female?

There is a person behind a curtain - I do not know whether the person is female or male. I know the person has long hair, and that 90% of all people with long hair are female I know the person has a ...
12answers
2k views

### What is the most surprising characterization of the Gaussian (normal) distribution?

A standardized Gaussian distribution on $\mathbb{R}$ can be defined by giving explicitly its density: $$\frac{1}{\sqrt{2\pi}}e^{-x^2/2}$$ or its characteristic function. As recalled in this ...
3answers
1k views

### Why law of large numbers does not apply in the case of Apple share price?

Here is the article in NY times called "Apple confronts the law of large numbers". It tries to explain Apple share price rise using law of large numbers. What statistical (or mathematical) errors does ...
8answers
4k views

### What is Bayes' theorem all about?

What are the main ideas, that is, concepts related to Bayes' theorem? I am not asking for any derivations of complex mathematical notation.
14answers
2k views

### Are there any good movies involving mathematics or probability?

Can you suggest some good movies which involve math, probabilities etc? One example is 21. I would also be interested in movies that involve algorithms (e.g. text decryption). In general "geeky" ...
4answers
1k views

### Probability of not drawing a word from a bag of letters in Scrabble

Suppose you had a bag with $n$ tiles, each with a letter on it. There are $n_A$ tiles with letter 'A', $n_B$ with 'B', and so on, and $n_*$ 'wildcard' tiles (we have \$n = n_A + n_B + \ldots + n_Z + ...
2answers
881 views

### Does the distribution $\log(1 + x^{-2}) / 2\pi$ have a name?

I ran across this density the other day. Has someone given this a name? $f(x) = \log(1 + x^{-2}) / 2\pi$ The density is infinite at the origin and it also has fat tails. I saw it used as a prior ...
6answers
896 views

### How likely am I to be descended from a particular person born in the year 1300?

In other words, based on the following, what is p? In order to make this a math problem rather than anthropology or social science, and to simplify the problem, assume that mates are selected with ...
5answers
3k views

### Convergence in probability vs. almost sure convergence

I've never really grokked the difference between these two measures of convergence. (Or, in fact, any of the different types of convergence, but I mention these two in particular because of the Weak ...
1answer
878 views

### Differences between a statistical model and a probability model?

Applied probability is an important branch in probability, including computational probability. Since statistics is using probability theory to construct models to deal with data, as my understanding, ...
3answers
404 views

### Elementary statistics for jurors

I have been summoned for jury duty. I am conscious of the relevance of statistics to some jury trials. For example, the concept of "base rate" and its application to probability calculations is ...
3answers
2k views

### Amoeba Interview Question

I was asked this question during an interview for a trading position with a proprietary trading firm. I would very much like to know the answer to this question and the intuition behind it. Thank you! ...
3answers
918 views

### Logistic Regression and Dataset Structure

I am hoping that I can ask this question the correct way. I have access to play-by-play data, so it's more of an issue with best approach and constructing the data properly. What I am looking to do ...
4answers
621 views

### How often do you have to roll a 6-sided dice to obtain every number at least once?

I've just played a game with my kids that basically boils down to: whoever rolls every number at least once on a 6-sided dice wins. I won, eventually, and the others finished 1-2 turns later. Now I'm ...
2answers
656 views

### Meaning of p-values in regression

When I perform a linear regression in some software packages (for example Mathematica), I get p-values associated with the individual parameters in the model. For, instance the results of a linear ...
3answers
289 views

### K successes in Bernouli trials, or George Lucas movie experiment

I'm reading "The Drunkard's Walk" now and cannot understand one story from it. Here it goes: Imagine that George Lucas makes a new Star Wars film and in one test market decides to perform a crazy ...
3answers
304 views

### How can I estimate the probability of a random member from one population being “better” than a random member from a different population?

Suppose I have samplings from two distinct populations. If I measure how long it takes each member to do a task, I can easily estimate the mean and variance of each population. If I now hypothesise ...
3answers
382 views

### Confidence Interval for variance given one observation

This is a problem from the "7th Kolmogorov Student Olympiad in Probability Theory": Given one observation $X$ from a $\operatorname{Normal}(\mu,\sigma^2)$ distribution with both parameters ...
3answers
3k views

### Extending the birthday paradox to more than 2 people

In the traditional birthday paradox the question is "what are the chances that two or more people in a group of n people share a birthday". I'm stuck on a problem which is an extension of this. ...
4answers
267 views

### The operation of chance in a deterministic world

In Steven Pinker's book Better Angels of Our Nature, he notes that Probability is a matter of perspective. Viewed at sufficiently close range, individual events have determinate causes. Even a ...
2answers
330 views

### Combining classifiers by flipping a coin

I am studying a machine learning course and the lecture slides contain information what I find contradicting with the recommended book. The problem is the following: there are three classifiers: ...
2answers
397 views

### Statistics, war stories, data intuition

I think it is fair to say statistics is an applied science so when averages and standard deviations are calculated it is because someone is looking to make some decisions based on those numbers. Part ...
2answers
613 views

### Can two random variables have the same distribution, yet be almost surely different?

Is it possible that two random variables have the same distribution and yet they are almost surely different?
5answers
213 views

### Does this quantity related to independence have a name?

Obviously events A and B are independent iff Pr$(A\cap B)$ = Pr$(A)$Pr$(B)$. Let's define a related quantity Q: $Q\equiv\frac{\mathrm{Pr}(A\cap B)}{\mathrm{Pr}(A)\mathrm{Pr}(B)}$ So A and B are ...
5answers
423 views

### Is there more to probability than Bayesianism?

As a student in physics, I have experienced the "Why I am a Bayesian" lecture perhaps half a dozen times. It is always the same -- the presenter smugly explains how the Bayesian interpretation is ...
4answers
430 views

### Do negative probabilities/probability amplitudes have applications outside quantum mechanics?

Quantum Mechanics has generalized probability theory to negative/imaginary numbers, mostly to explain interference patterns, wave/particle duality and generally weird things like that. It can be seen ...
3answers
651 views

### What is a tight lower bound on the coupon collector time?

In the classic Coupon Collector's problem, it is well known that the time $T$ necessary to complete a set of $n$ randomly-picked coupons satisfies $E[T] \sim n \ln n$,$Var(T) \sim n^2$, and \$\Pr(T ...
4answers
532 views

### Why is statistics useful when many things that matter are one shot things?

I don't know if it's just me, but I am very skeptical of statistics in general. I can understand it in dice games, poker games, etc. Very small, simple, mostly self-contained repeated games are ...
1answer
168 views

### Deriving Negentropy. Getting stuck

So, this question is somewhat involved but I have painstakingly tried to make it as straight-forward as possible. Goal: Long story short, there is a derivation of negentropy that does not involve ...
1answer
445 views

### Probability inequalities

I am looking for some probability inequalities for sums of unbounded random variables. I would really appreciate it if anyone can provide me some thoughts. My problem is to find an exponential upper ...
4answers
1k views

### What is so cool about de Finetti's representation theorem?

From Theory of Statistics by Mark J. Schervish (page 12): Although DeFinetti's representation theorem 1.49 is central to motivating parametric models, it is not actually used in their ...
5answers
463 views

### Confidence interval and probability - where is the error in this statement?

If someone makes a statement like below: "Overall, nonsmokers exposed to environmental smoke had a relative risk of coronary heart disease of 1.25 (95 percent confidence interval, 1.17 to ...
4answers
890 views

### What is a purpose of characteristic functions?

I'm hoping that someone can explain, in layman's terms, what a characteristic function is and how it is used in practice. I've read that it is the Fourier transform of the pdf, so I guess I know what ...
1answer
779 views

### What is the real answer to the Birthday question?

"How large must a class be to make the probability of finding two people with the same birthday at least 50%?" I have 360 friends on facebook, and, as expected, the distribution of their birthdays is ...
2answers
241 views

### What's the name of this discrete distribution (recursive difference equation) I derived?

I came across this distribution in a computer game and wanted to learn more about its behaviour. It comes from the decision as to whether a certain event should occur after a given number of player ...
3answers
231 views

### How do you tell whether good performances come in streaks?

I solve Rubik's cubes as a hobby. I record the time it took me to solve the cube using some software, and so now I have data from thousands of solves. The data is basically a long list of numbers ...
1answer
219 views

### Is it worthwhile to publish at the refereed wiki StatProb.com?

Background I read about StatProb.com from a comment on Andrew Gelman's Blog. According to the website, StatProb is: StatProb: The Encyclopedia Sponsored by Statistics and Probability ...
1answer
337 views

### How to predict when the next event occurs, based on times of previous events?

I'm a high school student and I'm working on a computer programming project, but I don't have a lot of experience in statistics and modeling data beyond a high school statistics course so I'm kinda ...
1answer
240 views

### How should I mentally deal with Borel's paradox?

I feel a bit uneasy with how I've mentally dealt with Borel's paradox and other associated "paradoxes" dealing with conditional probability. For those who are reading this that aren't familiar with ...
3answers
165 views

### Build a path probability tree for journeys through a website

I'm currently doing analysis on a website which requires that I create a decision tree diagram showing the likely route that people take whenever they arrive on the website. I am dealing with a ...
1answer
488 views

### What is this “maximum correlation coefficient”?

A typical image processing statistic is the use of Haralick texture features, which are 14. I am wondering about the 14th of these features: Given an adjacency map $P$ (which we can simply view an ...
3answers
561 views

### The prestige magician paradox

You probably know the trick in the movie the prestige : A magician has found an impressive magic trick : he goes into a machine, close the door, and then disappears and reappears in the other side of ...
5answers
929 views

### Time taken to hit a pattern of heads and tails in a series of coin-tosses

Inspired by Peter Donnelly's talk at TED, in which he discusses how long it would take for a certain pattern to appear in a series of coin tosses, I created the following script in R. Given two ...
3answers
921 views

### How to compute the probability associated with absurdly large Z-scores?

Software packages for network motif detection can return enormously high Z-scores (the highest I've seen is 600,000+, but Z-scores of more than 100 are quite common). I plan to show that these ...
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