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

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about the definition of bayesian network

In this PDF http://people.csail.mit.edu/yks/documents/classes/mlbook/pdf/chapter2.pdf page 5 says: given a set of function $f(x_i,pa(x_i))$ non negative and sum to 1, we define a joint probability as ...
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39 views

Is my learnings in Machine Learning fine? [on hold]

I am a self learner in Machine Learning. I am from humanities background. My goal was to know bit of Machine Learning and to develop few applications based on few algorithms. To get feel of the ...
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2answers
22 views

Probability of picking numbers

I am doing an introductory course in statistics and I'm struggling with one question in particular. The question is: Suppose two people each have to select a number from 00 to 99 (therefore 100 ...
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0answers
20 views

Hidden Markov Models relationship

I have a question regarding a small investigation that I have been conducting into the relationship between the length of observation sequence, T, on which two decoders (BCJR and classic Viterbi) ...
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1answer
19 views

Test for differences in 2 distributions and account for a random effect

I have two probability distributions and want to say that they are statistically different. Typically, I would use a K-S test. But, my data comes from multiple individuals, which suggests I have a ...
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4answers
162 views

What is the intuition behind the independence of $X_2-X_1$ and $X_1+X_2$, $X_i \sim N(0,1)$?

I was hoping someone could propose an argument explaining why the random variables $Y_1=X_2-X_1$ and $Y_2=X_1+X_2$, $X_i$ having the standard normal distribution, are statistically independent. The ...
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0answers
36 views

Can ayone help me in solving the below Problems of probability distribution?

Patients arrive randomly and independently at a doctor's surgery from 8·0 A.M. at an average rate of one in Five minutes.The waiting room holds 2 persons. What is the probability that the room will be ...
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1answer
56 views

Determining beta distribution parameters $\alpha$ and $\beta$ from two arbitrary points

Suppose I have two points $(p_1,x_1)$ and $(p_2,x_2)$ where $p_i$ is a probability on the beta CDF and $x_i$ is a value on that same CDF. How would I go about determining the beta distribution shape ...
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15 views

Need help on how to interpret Gamma Probability density function of gamma(2, 1/10) [duplicate]

The below sample graph was created using R, for an example I came across while reading (on Distribution of time until customer x arrives): ...
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1answer
113 views

How to compute this conditional probability in Bayesian Networks?

I met a problem related to conditional probability from the article "Bayesian Networks without Tears"(download) on page 3. According to the Figure 2, the author says $$P(fo=yes|lo=true, ...
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0answers
34 views

Problem with Finding Likelihood: Bayesian

I am really unfamiliar with Bayesian methods particularly parameter estimation. Suppose I have a test to find a parameter, theta which is the number of packaged bag for retail sale that could contain ...
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0answers
13 views

how do I calculate the probabiity of a match based on similarity of binary events?

I have 35 binary events (presence/absence coded as 1/0) that describe 7 questioned samples (QS 1...7) and 1 known sample (KS). I am asked to provide a probability (in percentage) of how likely it is ...
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1answer
48 views

Does the parameter change during data generation in Bayesian Inference?

Let's assume that we have the following graphical model: This graph encodes the joint distribution $P(p,x_1,x_2,x_3,x_4) = P(p)\prod_{i=1}^{4}P(x_i|p)$. In the Bayesian inference, if we know ...
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0answers
24 views

Are the events dependent? [on hold]

A die is rolled.. Event A- getting even numbers. Event B- getting non-perfect square numbers. Are the events dependent or independent? Why?
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0answers
46 views

Is my interpretation of Bayesian probability and inference correct?

I have the following interpretation of the Bayesian probability and inference (without referring to Measure Theory, I am still at the very beginning of learning it): Let's say we have five random ...
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1answer
34 views

Probability of 4 people placed in 3 rooms

A family consisting of four persons—A, B, C, and D—belongs to a medical clinic that always has a doctor at each of stations 1, 2, and 3. During a certain week, each member of the family visits the ...
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11 views

Optimal Number of Entries in Contest of Skill

Objective: I'm looking for the optimal number of unique entries in a contest of skill with monetary prizes. Description: The contests vary from as little as 20 entries up to 10,000+ entries. You ...
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1answer
36 views

simply demostration on conditioned probability

I don't find the answer of this simply problem: how can I algebrically demonstrate that, with 3 variable A,B,C $ \sum\limits_C P(B|C)P(C|A)=P(B|A)$ under condition that $P(A,B,C)=P(A|C)P(B|C)P(C)$ ...
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1answer
49 views

Annual Probability of Occurrence

I am trying to determine, based on historical record, what the annual probability of occurrence would be for a specific hazard. Take tornadoes. Over a 59 year time span I have documented 45 tornadoes. ...
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14 views

estimator(preferably unbiased) of $\ln E[X]$ [duplicate]

Given the distribution function of random variable $X$ I know how to estimate its mean. What would be an estimator(preferably unbiased) of $\ln(E[X])$ ?
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18 views

Wilcoxon rank sum test for significant differences between two time points

I have data like so …(Col1:Companyname Col2:Data at timepointA; Col3:replicate Data at timepointA; Col4:Data at timepointB; Col5:replicate Data at time point B ...
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66 views

How many eligible bachelors in a city?

This is a very simple question posed to me by a friend of mine. I know it's a statistical analysis problem, but I suck at math. Given the total population of $x$ within a metropolitan area, what ...
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1answer
23 views

What is the difference between dexp and pexp [duplicate]

I understand probability distribution but I am having a hard time getting a grasp on probability density function, specifically difference between dexp (density of exponential distribution) and pexp ...
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19 views

Probabilistic interpretation of regression for justifying squared loss function

I was reading Andrew Ng's CS229 lecture notes (page 12) about justifying squared loss risk as a means of estimating regressions parameters. Andres explains that we first need to assume that the ...
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0answers
16 views

Compute the total variation for multinomial distributions

Suppose I have two discrete random variables, $P$ and $Q$, with probability mass functions given by $p(x)$ and $q(x)$. I know that these random variables are multinomials, generated by choosing $K = ...
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7 views

sample generative model from a chain/tree

I have a tree of states and I would like to sample from this tree based on pure birth process; however, I don't know how exactly I can do this; so far I have done this; I simplified my problem; the ...
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1answer
62 views

Probability of assigning balls into buckets, where each bucket has a certain capacity

I'll start with a specific example of what I am trying to solve: I have eight balls to be randomly placed into four buckets. Buckets #1-3 have the capacity of 2, 2, 3 respectively, while bucket #4 ...
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0answers
8 views

Given MTTF and Number of Items, how to calculate failing parts with Time?

I am wondering how to make use of MTTF Here is the situation, I am given an MTTF for an item type x and a certain demand for that item in the next 25 years, say 100 parts that will be in operation ...
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1answer
131 views

If P(A)=0, is A a null event?

I know that P(null event)=0, but is the reverse true? i.e. if P(A)=0 is A a null event? I'm not too sure I even understand what a null event is, to be honest. Could anyone give me an example of one?
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24 views

How calculate average probabilities in MLP or SVM?

I have a system that find best model (best inputs and parameters of MLP/SVM) model in a financial problem for every inserted database and create a specific model for a specific data sample. I'm using ...
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57 views

Calculation of an overall top X over several groups

I'm not a statistics expert, so I'm hoping someone here can lend me a hand. I've got a bunch of key-value pairs associated with a specific time range. Something like this: ...
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13 views

Relation between electability and probability

Is the meaning of 'electability' the same as 'probability' to win? The way I understand it right now, when a survey says "Obama's electability is 63% means: there's X chance (?) that Obama will obtain ...
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2answers
63 views

Given a series of past coin tosses from an unfair coin, how can I calculate the confidence for the next toss result?

So this is really difficult for me, but I would like to know if this is possible. Let's assume I have an unfair coin (absolutely no assumptions can be made about the coin), and my past result has ...
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31 views

Threshold for psychometric experiment with three (or more) possible choices

I'm running an experiment where subjects are viewing a stimulus, and they have to decide if the stimulus is brighter/darker/identical in respect to a standard image. Stimulus luminosity actually ...
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1answer
31 views

Probability of $k$ successes in no more than $n$ Bernoulli trials

I feel like these questions should be related to the binomial and geometric distributions, but I can't quite work out how. Suppose I do sequential independent Bernoulli trials each with success ...
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1answer
138 views

Will I go to UC Berkeley?

I forget where I got this data (I think from About.com College), but here are some statistics regarding University of California, Berkeley admissions: the 25th percentile SAT Reasoning Test score was ...
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1answer
13 views

Difference between full house and two pair in consideration of numbers chosen?

So I am a bit confused about why the number of ways to get a full house is: $ 13 \choose 1 $$ 12 \choose 1$$ 4 \choose 3$$ 4 \choose 2$ as opposed to: $ 13 \choose 2 $$ 4 \choose 3$$ 4 \choose 2$. ...
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1answer
46 views

Finding distribution function [duplicate]

Let $X_1,X_2,...$ denote iid random variables such that $X_1$ is continuously distributed with density $p(x)$ and distribution function $F(x)$ where $F(0) = 0, F(x) > 0$ for all $x > 0$, and ...
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19 views

What is the correct definition for completness in d-separation in directed graphical models?

I was reading Koller's book of probabilistic graphical models and in section 3.3.2 she discusses what properties should hold for d-separation as a method for determining independence. She tries to ...
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2answers
107 views

Multivariate Bayesian formula

I got there example graphs bishop's PRML (8.2.1) 1. a <- c -> b $$ p(a,b,c) = p(a|c)p(b|c)p(c) --(1)\\ p(a,b) = \sum_c p(a|c)p(b|c)p(c) --(2) $$ Q1: Can I use a new graph to represent the ...
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1answer
19 views

Bidding Collusion Question: Probability of Identical Bids

I was asked this question. My initial conclusion is that there isn't enough information to calculate the probability. I would appreciate it if anyone could provide provide their insight. Scenario: ...
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1answer
57 views

Probabilty of getting an open-ended straight draw in 5 cards

I play Hold'Em on an internet site and it seems that far too often I see 4 sequential cards being flopped in the full 5 card flop; which is an easy setup for at least one of the players to make a ...
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36 views

probability that a variable is ONE OF the top k out of n when ordered

Suppose ($h_1,h_2,...,h_n$) is an $n\times 1$ vector. Let $h_i=g_iX_i$, where $g_i$ is a non-random variable which can vary across $i$ and $X_i$ is a random variable with Pareto Type I distribution. ...
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3answers
45 views

Biased coin toss simulation — which random generator is most appropriate?

I have a doubt whether the uniformly distributed random generator is the most appropriate to use for simulating biased coin toss. ...
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12 views

web analytic: average session length based on visits numbers per minute

At hand, I only have the number of visits per minute for one web page (one day period), is it possible to generate the average session length of such page based on these numbers? Or and references I ...
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23 views

Estimate SVM a posteriori probabilities with platt's method does not always work

I have a problem.. I'm trying to create a multiclass SVM with probability output. The SVM is working so far, what means, that the accuracy is ok (see the last picture). But the probability estimation ...
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1answer
25 views

Simulating outcome of 3 political parties

First I'm sorry I couldn't figure out the most accurate title for this question (suggestions welcome). Here's the case: I want to implement spinners like the ones on this page: ...
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1answer
59 views

how calculate inflation observed and expected p-values from uniform distribution in QQ plot

I am trying to quantify degree of inflation (ie. how best the observed data points fit to expected). One way is too look at QQ plot. But I would like to calculate some numeric indicator for inflation ...
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1answer
41 views

Maximum expected difference between players when using 4d6 drop lowest

Players of a certain TRPG have characters with 6 ability scores, each ability score ranging from 3-18. One method of generating those is by rolling 4d6 drop lowest for each of the scores. That means ...
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29 views

Let F be a distribution function. Prove that X is a RV

Let $F$ be a distribution function on $(\Omega,\, \mathfrak{F},\, P)=\left((0,1),\ \mathfrak{B}(0,1),\ \lambda\right)$ where $\lambda$ denotes Lebesgue measure. Define $X:\Omega \to \mathbb{R}$ by ...