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

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mixed model vs. markov chain

I have a longitudinal data with multiple time points (measured twice every year). There was seasonal difference on the outcome variable of interest (BMIz) if using mixed model (where time points were ...
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1answer
21 views

How to evaluate a statistical test for fairness of a coin?

I suspect that a given coin is not fair, i.e that the probability of heads is not $\frac{1}{2}$. My question is not how we can prove the unfairness, but if we derive a test to check the fairness, How ...
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In confusion with a Bayesian statistical problem

I was learning some probability basics. I am stuck with a problem, that I need your help with in solving. An $e$-fair coin is a coin with probability of head $(\theta)$ in interval ...
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59 views

Basic problem in Bayesian inference

I have questions with the following Bayesian inference problem I found in the book by Bertsekas & Tsitsiklis (Introduction to Probability 2nd ed.). Problem is as follows (P.445, Problem 2): ...
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2answers
101 views

How many answers to memorize for a test?

Recently one of my friends asked me this deceivingly simple question: I have a midterm with a predetermined list of 15 possible questions. Out of the 15 questions only 7 will actually appear on ...
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20 views

Non specific order of probabilities in a time step

I'm simulating a random collision process. At each time interval I calculate the probability of a collision occurring between each object and all other objects in proximity. Currently if I wish to ...
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2answers
87 views

Set of expected values

I have a doubt, I'd like to calculate a the expected value of a set, let suppose I have a set of n points, every point $x_i$ has a probability $p_i$, the expected value of this set is the sum of all ...
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1answer
61 views

sum and product rules of probability

I am reading Bishop's Pattern Recognition and Machine Learning. In page 73, chapter 2.1. I can't understand the formula 2.19 : $$p(x=1|\mathcal{D})=\int_0^1 p(x=1|\mu)p(\mu|\mathcal{D})\text{d}\mu ...
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1answer
24 views

How to handle unseen features in a Naive Bayes classifier?

I am writing a naive bayes classifier for a text classification problem. I have a bunch of words and an associated label: ...
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18 views

Expectation of a generalization of Dirichlet distribution

For the standard Dirichlet, the expectation of $X_i$ is $\alpha_i/\alpha_0$, where $\alpha_0 = \sum_i \alpha_i$ (http://en.wikipedia.org/wiki/Dirichlet_distribution). I am considering the following ...
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1answer
21 views

Greater than 1 Naive Bayes Probabilities?

I am trying to train a Naive Bayes classifier. In addition to getting the most likely class as an output from the Naive Bayes classifier, I would also like to compute the probabilities associated with ...
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1answer
16 views

Getting expected value of future value with time varying data (credit card revolving and fee data) . Customer lifetime value

I have a credit card data and that contains monthly amount of revolving and amount of fee for each customer. As a bank perspective, I want to get the expected value of future revolving amount and fee ...
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1answer
32 views

Convert Cross Correlation to Probability value

How can I convert the [-1;1] bound cross correlation value to a probability [0;1]. Cross correlation measures the similarity of two signals / images A,B, I aim at expressing this in the probability ...
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1answer
45 views

Bounded expectation implied bounded conditional or vice versa?

If $\mathrm{E}\left(X\right)<\infty$ does that imply $\mathrm{E}\left(X|Y\right)<\infty$? How about vice versa? I'm thinking if we condition on an event (say $Y>2$) then if we have ...
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12 views

Draw a possible realization [closed]

Consider a postoffice with only one server and a random arrival process of single arriving customers. Every customer requires a random service time and the queueing discipline is fist-come first-served. ...
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1answer
36 views

Probability statement with a confidence interval

Suppose you construct a 95% confidence interval on a mean. Can you state that there is a 97.5% probability that the true population mean lies below the CI upper bound and that there is a 97.5% ...
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2answers
81 views

Probability that a sum of potential numbers is greater than some value

Say I am about to receive 5 cash prizes and I have the probability of receiving each cash prize. Let's denote a set of cash prizes with $k$. So, below is the set of cash prizes and the set of ...
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2answers
67 views

Convergence in distribution of sum implies marginal convergence?

Let $X_n, X, Y$ be random variables such that $X_n + cY \stackrel{d}{\rightarrow} X + cY $ for every positive constant $c$. Prove that $X_n \stackrel{d}{\rightarrow} X$. I know if only we have joint ...
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29 views

CDF/ ECDF plot for data with two attributes

I have a data in the following format: $$ \begin{array}{rr} \textbf{colm_1} & \textbf{colm_2}\\ 3 & 1\\ 10 & 0\\ 3 & 0\\ 100 & 1\\ . & .\\ . & . \end{array} $$ colm_1 are ...
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1answer
24 views

Expected coverage of a set of random samples

For a set A, I'm running 8 independent random samples, each with a probability of 1/8=12.5% and is without replacement. I know that the set formed by the union of these 8 samples will be of a size ...
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12 views

Approximation of Gauss Hypergeometric function [closed]

I have a non-convex optimization problem due to this Hypergeometric function: $_2F_1(a,k;a+b;z)$. I am looking for an approximation of this function with convex function(s).Any idea ? Thanks!
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23 views

Creating statistically balanced teams

Suppose that you have a tournament for a game with four players on each team. We also have a table that tells us overall statistics for each player. This table includes things like each player's # ...
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80 views

Distribution function of maximum of n iid standard uniform random variables where n is poisson distributed

I am studying probability theory on my own and am trying to work the following problem in the book - Let $X_1, X_2, . . .$ be independent, $U(0, 1)$-distributed random variables, and let $Nm \in ...
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10 views

Difference between cross-correlations for two random variables and two probability functions.

Let me ask basic questions. Q1) What is the difference between cross-correlation between two random variables and cross-correlation between two probability functions for the two random variables? ...
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28 views

Interpretation of Linear SVM Coefficients [duplicate]

I’m building a model using Linear SVM from the Scikit-learn package in Python. I have found that Linear SVM performs much better on my training set than Logistic Regression. My question is, is there ...
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Actual value falling within prediction interval rather than predicted value falling within actual value range?

I'm trying to predict a price for an item on the website. I'm interested in classifying the prediction as good or bad. There are two approaches that I can think of, and I'm wondering which one is ...
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1answer
49 views

What is a cumulative Binomial probability?

I am new to this so don't know if I am asking the right question as I just read about its usage but didn't know what exactly a cumulative Binomial probability is. So my question is: What are ...
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34 views

Probability of vector similarity wrt dimensionality

I'm trying to show that the probability that two vectors are similar to each other increases as the number of dimensions decreases. I define similarity between two vectors $a = [a_1, a_2, ..., a_n]$ ...
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21 views

Calibration in Statistics [duplicate]

I would like to know how to, given a data set, obtain the following: 1/ The parametric probability density function that best explains the data 2/ The parameter values of such pdf Thanks Jonny
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2answers
47 views

Do multiple observers increase the probability of detecting an event?

I will describe my question with an example: A machine manufactures toys and places them on a conveyor belt. A toys expert overlooking the conveyor belt observes the toys. If a toy is faulty he can ...
2
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1answer
28 views

probability of tally having a count of 0 in x variables after sampling with replacement

I am a non-statistician testing a randomising algorthm. If I have a sample of size 100 (numbered balls) with replacement and that 50 such samples are independently drawn. To my understanding, the ...
4
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1answer
52 views

Probability estimation of minesweeper undecidable choices

Someone asked what was his probability to win in this situation? This is an interesting problem and I'll be curious to know an efficient solution. So far, I wanted also to generalize, with a ...
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1answer
101 views

What does it mean “being normally distributed”

There is an exercise which is used to illustrate how normal distribution works. The exercise starts by saying "Suppose scores on an IQ test are normally distributed..."; What does it mean for the ...
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39 views

Quantifying Potential for Violence/Espionage

I am planning a seven-question Likert-type survey with a "1 to 10" scale. The questions I am asking in the survey are to assess an individual's risk factors (how much risk they present to an ...
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19 views

Combining independent Gaussian probabilities

I am using three Gaussian distributions with which I generate random numbers to represent many candidate xyz points. I use some selection criteria (details not particularly relevant) to decide on ...
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1answer
92 views

Plain english explanation of the Rayleigh distribution?

I need to understand the Rayleigh distribution for a homework assignment in computer networks. Unfortunately, I lack the background knowledge in the field of statistics and probability theory to ...
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3answers
410 views

Do the pdf and the pmf and the cdf contain the same information?

Do the pdf and the pmf and the cdf contain the same information? For me the pdf gives the whole probability to a certain point(basically the area under the probability). The pmf give the probability ...
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12 views

Upper Bound on Mutual Information

I was advised to post this question here rather than in the math stack exchange. So here it is: I am interested in an upper bound on mutual information that I have been encountering frequently in the ...
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2answers
28 views

Probability generating function for negative values of random variables?

What if we have negative integral values for a random variable?Then is it possible to write a probability generating function for it? All definitions I have seen so far is for non negative integer ...
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1answer
42 views

Advantage of multiple simulations in old-fashioned Monte Carlo?

The spirit of this question comes from "Ordinary Monte Carlo", also known as "good old-fashioned Monte Carlo" Suppose I have a random variable $X$, with $$\mu := E[X]\\ \sigma^2:=Var[X] $$ Both are ...
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23 views

Sum of very low probability

I have a score of some feature, $F_1$ and $F_2$ where this score is the logarithm of probability. This score is very low and very sparse, for example i have: $F_1$ with score $-800$ $F_2$ with ...
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36 views

Most Important Stat Theory Concepts — Interview [duplicate]

I have an interview with a top company for a data scientist position. I was made aware that they will be testing probability/statistical theory concepts. So the question: If you had 1 hour tops ...
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2
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1answer
51 views

Moment generating function if the PDF is $f_z= Cz^{k-1}(1-\frac{z}{d})^bF(-a+k+1,b;b+1;1-\frac{z}{d})$

Let $z$ a random variable with PDF : $f_z= Cz^{k-1}(1-\frac{z}{d})^bF(-a+k+1,b;b+1;1-\frac{z}{d})$, where $0\leq z \leq d$, $F$ is the Hypergeometric function, $k$ is a positive integer, $-a+k+1 ...
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26 views

Stratified random sampling and its distribution

I'm learning stratified random sampling and I'm having hard time to solve this problem. consider the following population of six units: ...
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1answer
226 views

Probability of seeing k faces that appear more than 3 times when rolling 10 dice

Suppose I roll 10 dice (six-sided). What is the probability of seeing k faces that appear more than (or equal to) 3 times? For example, if I see 1, 1, 1, 2, 2, 2, 3, 4, 5, 6 then I have observed 2 ...
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19 views

Measure of probability of obtaining a certain $\chi^2$ given the number of trials

I am calculating an equation with several random components a large number of times, and in order to select my final answer I choose that with the minimum value for $\chi^2$. I am hoping to find some ...
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32 views

Conditional or Joint Probability under Various distributions

In various statistical models the baseline equation (like in Naive Bayes $$\mathrm{classify}(f_1,\dots,f_n) = \underset{c}{\operatorname{argmax}} \ p(C=c) \displaystyle\prod_{i=1}^n p(F_i=f_i\vert ...
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How to compute the marginal probability form conditional probabilities in logspace?

Normally the marginal probablity is computed as $p(x) = \sum_y p(x | y) \cdot p(y) $ Now, suppose I have all these probabilities at the right-hand side in logspace (so as logprobabilities). How do ...
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Law of iterated expectations - an small exercise

From edX MIT probability course - Widgets and Crates: Let $X_i$ be the number of widgets in a particular box $i$. Let $N$ be the number of boxes in a crate. Assume $X$ and $N$ are independent, ...