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

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Three Events Problem Interpretation

So I am having trouble understanding what this problem is asking. (I am not asking someone to solve it but simply help interpret what the problem wants me to do.) The problem goes like this: "Let ...
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8 views

Estimating Probabilities from Stratified Table

Say I have data stratified by smoking status, where $Y=1$ is has lung cancer, $Y=0$ doesn't have lung cancer, and finally $D=1$ drinks alcohol, and $D=0$ doesn't drink alcohol. How do I estimate ...
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24 views

Distance between two probability distributions [on hold]

I would like to know if there is a "best" symmetrizing for Kullback-Leibler distance? I would also like to know what is the best measures for such distance other than K-L distance.
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1answer
100 views

Good textbook for a one semester “probability and statistics” course for computer enginering 1st year

I am looking for a good textbook for a one semester "probability and statistics" course for computer engineering 1st year university students (e.g. no calculus). Can you suggest? Calculus should not ...
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1answer
37 views

Stock Price Problem Question

It a simple school problem with five different parts. I understand a), b), c), and e); however I am very confused on what d) means. The problem goes like this: "Suppose that each day the price of a ...
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3answers
102 views

Conditional Probability with Normal Distributions?

Let's say that I have $3$ independent random normal variables, $A$, $B$ and $C$. They all have a standard deviation of $17.526$, while $A$ has a mean of $143$, $B$ of $139$, and $C$ of $129$. My ...
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0answers
15 views

Logistic Regression with different priors

I am using standard logistic regression for classification with reasonable results. As expected I get a probability of 0.5 for query points "far away" from the data. However I would like to assign ...
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1answer
33 views

Probability of observing a false correlation and confidence limits

In oil and gas exploration/development it is common to use acustic impedance derived from reflection seismic surveys to predict the porosity measured in wells drilled in the reservoir. I often use ...
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1answer
20 views

Composition of bankruptcy probability and firm size

I'm using neural network for a binary classification problem of bankruptcy prediction using patternnet function in MATLAB, so i ...
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1answer
30 views

Run Many Small or a Few Big Simulations to Estimate the Mean?

I was just running some simulations on tossing a coin given certain conditions, to test out some ideas I had. I was trying to find the ratio $\frac{\mathtt{successful\ tosses}}{\mathtt{total\ ...
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2answers
91 views

What is meant by categorical distribution?

Is this separate type of distribution (EX: Binomial,bernoulli, Multinomial) or any distribution can be represented by this way. Can someone elaborate with simple example
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2answers
64 views

Probability of two aces given at least one ace (out of two cards) vs probability of two aces given one card is the ace of spades (out of two cards)

So, in the video lectures from Harvard's Statistics 110:Probability course that can be found on iTunes and Youtube, I encountered this problem. https://www.youtube.com/watch?v=JzDvVgNDxo8#t=566 I ...
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36 views

Finding the most “uniform” or “least concentrated” density function, subject to moment constraints

Background I want to find a probability measure for a continuous random variable, subject to moment constraints, that is maximally "uniform", as defined below: Definition: Maximally Uniform ...
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0answers
20 views

Evaluating the $H_0$ of a contigency table

I have a 2 way contigency table with variables $A=\{a_1,a_2\}$ and $B=\{b_1,b_2\}$. I have the observed cell frequencies $O_1=a_1b_1$, $O_2=a_1b_2$, $O_3=a_2b_1$ and $O_4=a_2b_2$. My null hypothesis ...
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1answer
20 views

Modelling a probability distribution on different feature sets

I have a binary classification problem, and I use method A and method B to extract features, F1 and F2, for this problem from dataset X. Now, I train two models, y1 and y2, separately on the two ...
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0answers
14 views

Calculate mutual information of twitter's users interactions

I have a research project about finding out user's interaction on Twitter. If I want to calculate the mutual information between two users A,B: I(A,B), to know the probability of A and B appearing in ...
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1answer
59 views

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 functions $f(x_i,pa(x_i))$ non-negative and sum to 1, we define a joint probability ...
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0answers
78 views

Is my learnings in Machine Learning fine? [closed]

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
24 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
24 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) ...
1
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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
220 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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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
61 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
127 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
45 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
50 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
50 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
36 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
38 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
53 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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15 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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72 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
24 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
17 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 ...
2
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1answer
65 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
10 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 ...
3
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1answer
136 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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26 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
64 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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0answers
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 ...