Questions tagged [probability]
A probability provides a quantitative description of the likely occurrence of a particular event.
12,103
questions
9
votes
3
answers
781
views
What does Jaynes' continuous pdf notation "$g(x)~\mathrm dx$" actually mean?
Something has been bugging me about E.T. Jaynes' treatment of continuous parameters.
In his book Probability Theory: The Logic of Science, uses notation that I am unfamiliar with when getting ...
- 275
7
votes
1
answer
2k
views
Probability of circles intersecting
Suppose that N circles are dropped randomly onto a square in 2-space in such a way that the center of each circle
lands somewhere in the square – even if some of the circle extends beyond the boundary ...
- 183
2
votes
2
answers
3k
views
Expected value of the reciprocal of a random variable
Given that $X$ is random variable that takes values:
$0,\dots,H-1$
The PMF of $X$ is unknown, but I can tell what is the expected value which is $\bar{X}$
There is event $Y$ when calculated it ...
- 29
0
votes
0
answers
189
views
the relationship between statistics and probability [duplicate]
Possible Duplicate:
What's the difference between probability and statistics?
Today I just came back from a student seminar in our department. And I heard that for the Pareto distribution, it ...
- 925
11
votes
1
answer
8k
views
If random variables are drawn from an identical distribution, why doesn't this guarantee they are independent?
Having read a little about exchangeability, I went back to thinking about the iid condition required for the central limit theorem. It struck me that if two random variables are drawn from an ...
- 121
6
votes
2
answers
59k
views
How to find P(X > F) in ANOVA F-test?
(Apologies for the ASCII tables, Stackexchange doesn't allow HTML tables and since I'm not supposed to link to an image, this is the only way I know of showing the data)
I'm learning about ANOVA F-...
- 251
2
votes
0
answers
511
views
What is the probability of a team winning many golf tournaments when conducted with handicaps (i.e., has sandbagging occurred)?
For non golfers, each golfer has a handicap based on his scoring history. The handicap predicts, on average, how many shots above par that golfer will take to play 18 holes. In theory, when that ...
- 21
9
votes
1
answer
472
views
How to compute $\mathbb P( 3 X_{(1)} \geq X_{(2)}+X_{(3)})$ for order statistics of a uniform distribution?
I am trying to solve a problem for my thesis and I don't see how to do it. I have 4 observations randomly taken from a uniform $(0,1)$ distribution. I want to compute the probability that $3 X_{(1)}\...
- 91
3
votes
0
answers
389
views
Is it valid to model discrete numerical test scores as coming from a continuous random variable?
I'm working with a sample of test scores which range from 0 to 100. These scores are generated from a set of 100 binary responses (0 or 1), so the higher the resulting sum, the better the performance. ...
- 41
3
votes
0
answers
1k
views
Distribution of the size of overlap between two random samples with duplicates?
Similar to this question, I want to know if the overlap between two samples is significant. However, my items are not unique; I have $c$ distinct colors of items, there are $m_i$ items of color $i: (...
- 471
1
vote
1
answer
395
views
Simulating continuous distribution using discrete distribution
I have a continuous random variable $X$ (positive). I want to simulate its distribution with a discrete distribution and calculate $E[X]$ from that discrete distribution. So, the obvious approach is ...
- 249
3
votes
2
answers
250
views
Designing an inference engine for unknown items with known probabilities
I have done some AI projects involving inference, neural networks, etc., but I'm not sure what the right algorithm would be for this problem.
Say there is a set of pills, where each type is visually ...
- 31
4
votes
2
answers
1k
views
Different ways to calculate conditional probability of independent events
Say we have TWO tests for cancer. Each test has the same probabilities of being right/wrong for cancer/no cancer. What is the probability of getting two positive test results?
In what follows, I'll ...
- 143
27
votes
6
answers
2k
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 ...
- 331
10
votes
3
answers
1k
views
The prestige magician paradox
You probably know the trick in the movie The Prestige :
[MOVIE SPOILER] A magician has found an impressive magic trick: he goes into a machine, close the door, and then disappears and reappears in ...
12
votes
8
answers
10k
views
The prisoner paradox
I am given an exercise, and I can't quite figure it out.
The Prisoner Paradox Three prisoners in solitary confinement,
A, B and C, have been sentenced to death on the same day but, because
...
1
vote
1
answer
114
views
What is the probability of observing not more than N positive outcomes
I have the population which is split into three classes; A, B and C. We know that the number of observations in each class is Na, Nb and Nc respectively. Assuming that my observations are binary ...
- 7,011
2
votes
0
answers
165
views
Testing endogeneity against decision probability
I am working with a model where the literature suggests there is potential endogeneity between the dependent variable and the primary independent variable of interest (a binary treatment). However, ...
- 269
4
votes
1
answer
530
views
Balls with weight in an urn
I have $n$ balls in an urn labeled from $1$ to $n$ and each of them has weight equal to its label. A ball has probability of being picked proportional to its weight, i.e. if the total weight of the ...
- 215
7
votes
2
answers
153
views
Statistics on mathematical "data"?
Lets say there is a theoretical relationship you want to prove over all values of some variable.
For example, $F(x)$ increases with $x$.
You are unable to come up with a general theoretical proof. ...
- 1,049
10
votes
1
answer
415
views
Proving a sequence decreases (supported by plotting a large number of pts)
Many of the questions I've posted on SE in the last month have been in the goal of helping me solve this particular problem. The questions have all been answered, but I still can't come up with a ...
- 1,049
11
votes
1
answer
2k
views
Why do people use the term "weight of evidence" and how does it differ from "pointwise mutual information"?
Here, "weight of evidence" (WOE) is a common term in the published scientific and policy-making literature, most often seen in the context of risk assessment, defined by:
$$w(e : h) = \log\frac{p(e|h)...
- 165
3
votes
1
answer
169
views
A random censored regression problem?
Assume I have random variables $X$ and $Y$. $X$ is observable; $Y$ is not. We also know that, if $X \leq Y$, $Z = f(X,Y)$ where $Z$ is a third random variable and $f(\cdot)$ is a known function; ...
- 51
3
votes
2
answers
2k
views
If a sequence of distributions converges to a degenerate, does that imply the variance strictly decreases?
If $F_i = G(F_{i-1}), F_0 = x$ is a sequence of distributions that converges to a degenerate distribution as $i \to \infty$, does that imply that the variance of $F_i$ decreases with $i$?
...
- 1,049
20
votes
1
answer
7k
views
Notation conventions for random variables and their distributions
I get confused on the proper notations of meanings, as well as the meanings of some notations relating to random variables and their distributions. Below, I will list things that I think are true, as ...
- 1,049
4
votes
1
answer
149
views
Variance of a marginal order distribution less than the variance of the full distribution?
Is there a proof/theorem that states that
$$\mathrm{Var}(X_{kn}) \leq \mathrm{Var}(X)$$ where $X$ is a continuous random variable with distribution $F$, and $X_{kn}$ is the $k^{th}$ of $n$ order ...
- 1,049
4
votes
1
answer
745
views
Order statistic expectations and the variance of the original distribution
Is there a proof or theorem out there that says that the difference between the expectations of the order distributions of $n$ draws from a distribution $X$ decreases as the variance of $X$ decreases?
...
- 1,049
3
votes
1
answer
198
views
How to get started in data-relation algorithms and mathematics?
I am very interested in the concepts and discussions taking place here. However, I'm not entirely sure what this field of study is called or what the many branches of study are being discussed here ...
- 197
9
votes
5
answers
2k
views
Derive P(C | A+B) from Cox's two rules
I am working my way (self-study) through E.T. Jaynes' book Probability Theory - The Logic of Science
Original Problem
Exercise 2.1 says: "Is it possible to find a general formula for $p(C|A+B)$ ...
- 438
2
votes
1
answer
185
views
How to determine larger probability of drawing one element from a set when set size and number of draws with replacement vary?
Which is the better scenario in terms of probability with the following:
Scenario 1
I have a hat with 5 tickets in it (I have one).
There is one single draw.
I have a 20% chance that my ticket is ...
- 123
7
votes
2
answers
3k
views
Average number of failures before success
By the title, you must instantly think that it's a geometric probability distribution (or perhaps binomial, by the story below) that I'm looking for, but my stats is failing me. Allow me to put this ...
- 173
5
votes
1
answer
556
views
How are epidemic models simulated in case of mobility?
I don't know whether this is a pure statistics, math or programming question so kindly let me know if there is a better place to post this question.
I am trying to implement the SIS epidemic model ...
- 4,402
7
votes
1
answer
7k
views
How to solve Chuck-a-Luck puzzle
Story (spoilers!)
The puzzle:
Chuck-a-Luck is a gambling game often played at carnivals and gambling
houses. A player may bet on any one of the numbers 1,2,3,4,5,6. Three
dice are rolled. If ...
- 633
16
votes
2
answers
5k
views
Are the random variables $X$ and $f(X)$ dependent?
Can we say anything about the dependence of a random variable and a function of a random variable? For example is $X^2$ dependent on $X$?
- 561
8
votes
1
answer
490
views
Predicting total number of bugs based on number of bugs revealed by each tester
Assuming n testers were independently testing the same application for a given period. Each tester found a given set of bugs (Some of the bugs were detected by more than one tester).
For example:
...
- 380
20
votes
2
answers
6k
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 ...
- 301
2
votes
1
answer
2k
views
Some exercises related to sampling and the normal distribution
Following cardiac surgery, patients are encouraged to exercise regularly (assume that regular exercise is defined as exercising on 3 or more days per week). A physician suspects that patients exercise ...
teng
1
vote
2
answers
17k
views
Calculate average frequency of an event based on probability and number of chances per hour
I do not have any idea how to calculate this, but I do have the data points available.
I have a computer system that has a setting for something -- garbage collection ("gc") -- to occur with p ...
- 113
1
vote
0
answers
309
views
Understanding entropy/salience of probability distribution of two data sets
I'm using a 1.6M tweet corpus to train a naive bayes sentiment engine.
I am trying to "compute the entropy of a probability distribution of the appearance of an n-gram in different datasets"....
- 111
2
votes
1
answer
354
views
Probability of throwing same sequence of 13 heads or tails
Simple (I hope) probability question I'd love it if someone could answer for me.
You flip a coin 13 times (two outcomes: heads or tails).
Before the coin tossing, I've written down the 'winning ...
- 29
3
votes
1
answer
219
views
Handling NLP probability results
I'm a programmer without a statistics background. I've been working with NLP lately to classify documents, and I'm pretty up to speed with NLP concepts. I've gotten to the point where the NLP ...
- 131
3
votes
2
answers
5k
views
Metric for probability based classification
I am doing a system for classifiying documents. The project demands the use of probability based output. So a sample will have a probability for belonging to each class.
For now I use logistic ...
- 33
16
votes
6
answers
5k
views
Probability theory books for self-study
Are there any good books that explain important concepts of probability theory like probability distribution functions and cumulative distribution functions?
Please, avoid referring books like "...
1
vote
0
answers
210
views
What's the difference between $p(x \mid \theta)$ and $p(x; \theta)$? [duplicate]
Possible Duplicate:
Meaning of probability notations $P(z;d,w)$ and $P(z|d,w)$
Can you tell me the difference between $p(x \mid \theta)$ and $p(x; \theta)$?
I know $p(x \mid \theta)$ is the ...
- 11
6
votes
4
answers
18k
views
Probability of two people meeting
Problem:
Two people are to arrive at the same location some time between 3pm
and 4pm. They both arrive at random times within the hour and only
stay for ten minutes. Since they only go one time, what ...
- 175
3
votes
2
answers
25k
views
Given P(A) and P(B), what would be the minimum probability of the intersection?
Like if I was given a P(A) of .5 and a P(B) value of .4 how would I get the minimum of the P(A∩B)?
- 41
2
votes
2
answers
499
views
When should I use $E(X)$ and when to use $\mu$ for the mean?
I see that $E(X)$ and $\mu_x$ are used to refer to the mean of some distribution or variate, but I am not clear on what circumstances each is appropriate.
$E(X)$ seems to always be more often in the ...
- 263
1
vote
1
answer
312
views
Probability in logistic regression
I come across a practice where the logit (Intercept + beta* variables) is once again input as a independant variable in a single variable logistic regression against dependant variable to get ...
- 29
4
votes
1
answer
1k
views
How to interpret the divergence of Fisher information expectation?
Consider translated Weibull distribution with probability density function:
$$
f(x ; k, \lambda, \theta) = \frac{k}{\lambda} \left( \frac{x-\theta}{\lambda} \right)^{k-1} \exp\left( - \left(\frac{...
- 407
9
votes
4
answers
23k
views
How to create a dataset with conditional probability?
Suppose that a certain disease ($D$) has a prevalence of $\dfrac3{1000}$. Also suppose that a certain symptom ($S$) has a prevalence (in the general population = people with that disease$ $D and ...
- 563