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

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Probability Question on Selection

I am currently doing a self-study question that gave me the following scenario: There are 10 marbles in a jar. 7 marbles are red while 3 are blue. John wants to pick 4 marbles out to give his friend. ...
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13 views

Drawing without replacement

An urn contains $X$ white balls and $Y$ black balls. What is expected number of balls you will draw before drawing a black ball? For example, if$X=2,\ Y=1$, the possible outcomes would be: ...
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22 views

Sum of multiple loaded dice

I have $n$ dice with $m$ sides. The $i^{th}$ dice will show value $0 \leq x_i \leq m-1$ with probability $0 \leq D_i(x_i) \leq 1$. What is the probability that the sum of the dice equals $\alpha$ Is ...
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12 views

Classification measures for linear classifier

Let $\mathcal{H}\colon\mathbf{w}\cdot\mathbf{x}+b=0$ be a separating hyperplane, which some binary linear classifier results in. Let $\mathbf{x}_t$ be an unseen, new sample that appears and needs to ...
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1answer
46 views

When to use Bayes' theorem to calculate conditional probability?

Given 2 events $E, F$, I know that $P(E | F) = \frac{P(E \cap F)}{P(F)}$. However sometimes the Bayes' theorem is used instead: $P(E | F) = \frac{P(F | E) P(E)}{P(F|E)P(E)+P(F|E^{c})P(E^{c})}$. ...
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23 views

MAP Estimator with Laplacian Noise

I need to calculate the MAP estimator of $ x $ in the following case: $$ \left [ \begin{matrix} {y}_{1}\\ {y}_{2} \end{matrix} \right ] = \left [ \begin{matrix} x\\ x \end{matrix} \right ] + ...
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48 views

Hammersley–Clifford theorem

I'm reading this paper http://image.diku.dk/igel/paper/AItRBM-proof.pdf and I got stuck in page 4 with equation (1) that's based on Hammersley–Clifford theorem. I'm not good in reading set theory ...
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12 views

Monte Carlo Integration Interval Probability

Use MC integration to estimate the probability that X * exp(X) < 2.5, assuming that X ~ Gamma(1.2,3.7) ...
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16 views

Rigorous Bell-CHSH?

The usual derivations by physicists of the Bell-CHSH inequalities as a limit imposed on any possible local hidden variables description of quantum systems seems so sloppy, that I'm tempted to ask you ...
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1answer
23 views

Probability of Two Samples Containing Overlapping Data

Quick question about sampling a data population that contains non-overlapping data: if I take two samples of 50 from a population of 100,000 unique data points, how would I calculate the probability ...
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34 views

Average minimum distance between two random vectors

Let $\mathbf{y_1} =\begin{bmatrix}g_1x_1 & g_2x_1 & \dots & g_Nx_1 \end{bmatrix}$ and $\mathbf{y_2} = \begin{bmatrix} f_1x_2 & f_2x_2 & \dots & f_Nx_2\end{bmatrix}$. All the ...
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4k views

Expected number of ratio of girls vs boys birth

I have came across a question in job interview aptitude test for critical thinking. It is goes something like this: The Zorganian Republic has some very strange customs. Couples only wish to ...
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1answer
28 views

How to calculate P(X=x|Y=y) using copula functions?

I want to get the conditional probability of P(U=u|V=v) or P(X=x|Y=y) using copulas.However, I found that if I use the copulapdf function of Matlab, the result is bigger than 1! I don't know why. any ...
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2answers
37 views

How can any statistics be calculated from a infinite population.

My understanding of some statistics: For a given experiment a finite number of samples can be taken, defining the sample size. However this experiment may have an infinity large population size. ...
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20 views

Calculating probability from missing/sparse sample

Given score(Q, R) = score obtained by person R for topic Q, where smaller value is better In an ideal scenario, I am given a set of data (events are mutually ...
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19 views

Probability of class membership given univariate normal distribution

Assuming a class is well described with a normal distribution of u and s, is it reasonable to calculate the probability of membership as: $Pr(x)=Pr(|x-u|)=2.0*\text{cdf}(|x-u|,s)$? I've briefly ...
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2k views

Help me calculate how many people will come to my wedding! Can I attribute a percentage to each person and add them?

I am planning my wedding. I wish to estimate how many people will come to my wedding. I have created a list of people and the chance that they will attend in percentage. For example ...
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1answer
53 views

Interpretation of Maximum likelihood estimation

I have some problem to interpret the result of MLE estimation : Is it possible to get some advise about how to interpret it? the log likelihood function : $\sum^{n}_{i=1}\log\left( \phi\left( ...
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12 views

What is the proper way to compare two estimated densities using sample data?

Say if have a dataset $X \subset \mathbb R^d$. I have two candidate probabilistic models M1 and M2 (e.g., M1 is a mixture of 2 gaussians and M2 is a mixture of 3 gaussians). I want to know which model ...
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11 views

sequential testing and hierarchical tesing

With respect to the hypothesis testing, I once heard sth such as sequential testing, hierarchical testing, and multi-level testing. But I could not find a good reference discussing these topics. Any ...
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1answer
29 views

How to bridge between seemingly unrelated but congruent PDF and PMF?

Let's assume a probability mass function $P$ on the discrete domain $\{0,...,N\}$ and a density function $f$ and the existence of two real factors $a$ and $b$ so that we have for all numbers $k$ in ...
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1answer
33 views

with Excel, generate 0 with n% probability OR generate 1 with (1-n)% probability

(first of all I simplified my question) depending on the input info below, I want to create proper excel function in output part. what I require verbally in output part under "status (0 or 1) ...
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21 views

Covariance when exponentiating a normal random variable [duplicate]

Say $Z \sim N(\mu, \sigma^2)$. I am trying to figure out what is the variance of $Y = exp(Z)$. The first thing that came to mind was approximate $exp(Z)$ with a second order taylor series, then it ...
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38 views

Package ‘fitdistrplus’

I am trying to use the package ‘fitdistrplus’ in R to fit one non standard distribution to my data set. I am trying to copy the methods the package creators used in their tutorial for specifying a ...
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23 views

Probability of classification given two observations

If two doctors each correctly diagnose a disease 55% of the time, and both agree in a certain case there is disease, what is the probability of disease? Surely it is higher than 55%?
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49 views

Determine the probability density function

I have the following problem. Let's say g is a function of A and R. I run a Monte Carlo ...
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99 views

If $X$ is normally distributed, can $\log(X)$ also be normally distributed?

Suppose $X$ is distributed $N(\mu, \sigma^2)$ where $\mu \neq 0$. Can I use the Delta Method to say that $log(X)$ ~ $N(log(\mu), \sigma^2/\mu^2)$?
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24 views

Handwriting Recognition - Percentage Match

I'm currently working on a senior project and we've chosen handwriting recognition. Initially I thought that using machine learning algorithms were a good idea for this, but after the thought below ...
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23 views

Assuming training data as set of target funtions

In this 10th slide of http://www.cs.cmu.edu/afs/cs.cmu.edu/project/theo-20/www/mlbook/ch6.pdf presentation The Training data set $D$ is assumed as the set of target function . Actually $D = ...
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24 views

Help understanding probability in simple random sampling

Quoted is an extract for Sample Survey Principles and Methods, Vic Barnett(2002) Pg 34 The concept of probability averaging only arises in relation to some prescribed probability sampling schemes. ...
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47 views

Formulas for probabilities in Bayes theorem

In continuation to this question $p(h|D) = \frac{p(D|h)p(h)}{p(D)}$ $p(h) = $prior probability of hypothesis $h$ $p(D)$ = prior probability of training data $D$ $p(h|D)$ = probability of $h$ ...
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Holder's inequality [migrated]

Given random variables $X$ and $Y$, Holder's inequality states that: \begin{equation} ||XY||_1 \leq ||X||_p ||Y||_q , \end{equation} for $\frac{1}{p} + \frac{1}{q} = 1$, and $p,q \in [1, \infty]$. ...
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16 views

Gamma Distribution MGF

I'm not sure how to find part a, what formula can be used to find this mgf?
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19 views

Question about the frequency definition of probability

In the book, it is written that the relative frequency or the frequency ratio gradually tends to become more or less constant as N becomes larger and larger. It is also mentioned that this is an ...
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1answer
57 views

Two easy probability tasks

I'm struggling with two exercises for which I do possess answers, but I have no idea why they would be like that. I haven't done any statistics in a long time (restarting studies). Question 1 Two ...
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21 views

Feature relationship based class separability

I am a computer science guy, not a mathematician so kindly excuse me if there is any ridiculous error in my problem description. I have two clusters $C_1$ and $C_2$ in a feature space spanned by $k$ ...
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22 views

What is the probability that the lot will be accepted even though it contains 20 defective fuses?

A collection of 100 fuses is inspected as follows: Five fuses are chosen at random and tested. If all five blow at the correct amperage, the lot is accepted. What is the probability that the lot will ...
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24 views

Probability of ongoing experiment

Suppose, I do a experiment where I have an event 'a' true 1000 times in 1000 trials. So, the probability becomes 1000/1000 = 1. If I am going to do another trial, my prediction about event 'a's ...
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1answer
32 views

Probability on Z-score

I have a data of 30 values that represent returns on investment and which have a mean of 7 and standard deviation of 14. We are talking here about normal distribution. Now I am being required to do a ...
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1answer
55 views

Likelihood vs. Probability

I have difficulties with Likelihoods. I do understand Bayes' Theorem $$p(A|B, \mathcal{H}) = \frac{p(B|A, \mathcal{H}) p(A|\mathcal{H})}{p(B|\mathcal{H})}$$ which can be directly deduced from ...
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2answers
132 views

Choosing a discrete non-uniform distribution for generating random integers

I have a list $l$ containing integers in the range $[1,max]$ On list $l$ I do an operation $isPresent(x)$ which return true if ...
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1answer
60 views

probability that a year has 53 mondays

We have the years from 2001, 2002, 2003,... to 2010. Say, a year is chosen at random from the listed years. What is the probability that the chosen year has 53 Mondays ?
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1answer
61 views

Using Poisson distribution to generate random integers

I'm trying to generate random integers which have Poisson distribution. The open source library GSL has one such distribution. Function: ...
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14 views

How can I determine the probability that a sample has a certain average given details about the total population?

Imagine that I have goal scoring data for a hockey team. They average 2.43 goals scored per game with a standard deviation of 1.63 for this data set. They have played 82 games. I have two subsets of ...
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56 views

Probability plot vs. QQ plot

What is the difference between probability plots and QQ plots when trying to analyse a fitted distribution to data?
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31 views

R package kernlab probabilities seem not to match decision

For a classification problem I am giving the R package kernlab a shot – not the least because it offers to calculate class probabilities instead of only a plain decision. However, comparing results ...
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480 views

Why maximum likelihood and not expected likelihood?

Why is it so common to obtain maximum likelihood estimates of parameters, but you virtually never hear about expected likelihood parameter estimates (i.e., based on the expected value rather than the ...
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3answers
58 views

Given two sets, how can I say statistically if they are similar/different

This is a very open ended question. Suppose I have two sets of data samples of the same form, say [item, rating]. Rating is a value on the interval [0,100] and item is a unique identifier given to a ...
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1answer
29 views

What is the distribution of a sum of a subset of probabilities, with each probability having the same distribution?

Suppose I have k outcomes with probabilities, pi, with p1+p2+...+pk=1. Each probability has the same distribution. What would the distribution of a sum of probabilities be? For example, what would the ...
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31 views

multivariate distributions bounded on [0,1] where parameters can be solved for from known mode

I need some kind of multivariate distribution which has the following properties support is $x_1,$ $x_2$, ..., $x_K$ where all $x_i \in [0,1]$ Though not required it is true that elements of the ...