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

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What's the Probability of having this Hypothetical Disease?

Question about disease transmission and infection: I want to know the odds of catching a disease and not knowing I have it, if the following conditions are possible: There is a 1/10,000 chance of ...
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13 views

Testing for consistency in survey data

I have a panel of 6 persons which each have generated 2 recipes (cooking), R1 and R2. I have then asked everyone in the panel to ...
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16 views

Sample of one, extermination of fruit flies and daily life challenges

First of all, I'm very well aware that a sample of one is ridiculous in any normal scenario in the domain of statistics, and I know that any rationale from this would probably only have esoteric ...
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1answer
98 views

drawing balls from an urn

Suppose there are 7 golf balls in an urn and you draw balls in 3 stages without replacement. First you draw 2, then 3, and then the remaining 2. How many ways are there to do this? I believe the ...
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1answer
32 views

Calculating feature probabilities for Naive Bayes

I'm reading "Building Machine Learning Systems with Python" by Willi Richert and Luis Pedro Coelho and I got into a chapter concerning sentiment analysis. There is a whole example about classifying a ...
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4answers
1k views

How to add odds? (or how I got the wrong sandwich)

Jon and Frank ordered 2 footlong sandwiches, but instead got 4 6-inch sandwiches. Jon had ordered spicy italian, and Frank chicken teriyaki. The sandwiches aren't labeled and are wrap, so they can't ...
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1answer
20 views

Is there a way to estimate the distribution from only a small number of outliers?

For example, I was looking at this list of the 93 people who have broken the "10-second-barrier", after reading that sprinter Christophe Lemaitre was the first person of purely European decent to ...
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2answers
31 views

Stuck on a proposition

Suppose four numbers $\{a,b,c,d\}$ where $a$ and $c$ random variables from a continuous distribution with support on $\mathbb{R}$. Does $b\neq d$ imply $|a−b|−|c−d|+a−c\neq 0$ almost surely? I ...
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65 views

Calculate $\mathbb{E}[Z_i]$ where $Z_i = \min(X_i, Y_{i-1})$, $X \sim Beta(\alpha,1)$

Let $X$ be a IID random variable with support in $[0,1]$ and CDF given by a Beta distribution, i.e. $X \sim \mathrm{Beta}(\alpha,1)$. Let $Z_i = \min(X_i,Y_{i-1})$, $\forall i >1$. I would like to ...
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46 views

Problem solving a simple probability exercise

I'm currently studying a Statistics course and I'm trying to solve a simple probability exercise: A production facility employs: 20 workers on the day shift 15 workers on the swing shift 10 workers ...
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1answer
48 views

Maximum convergence rate of empirical probability

Given a sequence of events $$(a_1, a_2, \dots, a_n),$$ then the sequence of empirical probabilities of some event $\alpha$ is $$\left(p_1 = \frac{\sum_{i = 1}^1 [a_i = \alpha]}{1}, p_2 = ...
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The probability that the 5th O+ donor is fourth of the day [closed]

If one-third of the persons donating blood at a clinic have a O+ blood, find the probability that the 5th O+ donor is the fourth donor of the day.
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1answer
29 views

prediction of polls

Just as an example Scotland has poll to decide whether they need to be independent from UK or not. Here is BBC's summary of different polls: ...
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20 views

Accuracy score for comparison of two probability grids

I would like to calculate an accuracy score for two grids. The cells of the grid have a probability of being occupied (1 = occupied, 0 = free). One grid is supposed to be the reference grid (blue) and ...
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0answers
24 views

Probability of input word

I have 2 text files containing certain sentences. I calculated the individual probabilities of every single word in both files. for file1: $$p(\text{A})=\frac{(\text{total occurrence of a word in ...
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1answer
44 views

What's the correct way to simulate a division winner?

So I'm trying to simulate one winner for each of the 4 NFL divisions, assuming that all teams are of equal ability. It's clear that the probability of each team being the division winner is $1/4$. I ...
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0answers
23 views

Occupancy octree metrics (Kullback-Leibler)

As I'm currently working on scan matching for outdoor environments I was wondering about the best metric to compare two occupancy octrees (one resulted from the scan matching and one ground truth ...
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1answer
36 views

How is this Negative Binomial Random variable used to solve this problem?

I was looking at the solution to this problem below and I don't understand how they used a negative binomial R.V. to solve the problem. A research study is concerned with the side effects of a new ...
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22 views

Word probabilities in a Naive Bayes filter

While implementing a Naive Bayes filter, I stumbled across a problem with the calculation of the conditional probabilities $p(w|c)$ of a word $w \in \mathcal{W}$ given a class $c \in \mathcal{C}$. ...
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1answer
18 views

Should the average prediction for a given attribute value equal the rate for that value?

Let's say I'm predicting the likelihood that someone will buy a widget, using their age, eye color, and gender as input attributes. I split my data into a training set and a test set, and train up my ...
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73 views

Suppose that A and B are mutually exclusive events for which P(A) = .3 and P(B) = .5

Suppose that A and B are mutually exclusive events for which P(A) = .3 and P(B) = .5. What is the probability that ...
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0answers
36 views

Can value of predicted probability from logistic model be greater than one?

I derived a multivariate logistic model from my data containing a single binary response and five predictors. I tried to calculate the predicted probabilities of one of the binary predictor ...
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34 views

When are correlation coefficients and variances not enough?

I am reading a paper and found the following, Statistical uncertainties and dependencies are often measured by variances and correlation coefficients, but both uncertainty and dependence can be ...
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35 views

Probability that one person's weight is more than 50 pounds greater than another's

The weight of a Portuguese man is normally distributed with mean 160 pounds and standard deviation 30 pounds. The weight of a Portuguese woman is normally distributed with mean 120 pounds and ...
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19 views

Scheduling Algorithm for a multi-server queue problem

I have 4 servers, n customers and m reports. At any time, a customer may request one of m reports. There are only 4 servers which are capable of generating reports. Each server can only process one ...
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1answer
54 views

Decompose (deconvolve) a 2-peaked pdf into 2 elementary pdfs

How could I decompose a two-peaked (empirical) pdf into 2 say lognormals or other appropriate pdf in a straightforward way? I'd prefer in Matlab. to something like this: Thanks!
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1answer
59 views

Using chi goodness of fit to test if data comes from normal distribution

The problem gives 50 observations and then asks to check whether the data comes from a normal distribution. For instance if these are your observations then how would you go about testing to see if ...
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36 views

E-mail answered probability after n days of waiting for a reply - based on a sample of e-mails and replies

Here is the task: I have a sample of replies to my e-mail from my mail box. A sample is taken over a period of 90 days, 1000 e-mails and replies if any. (We only consider a pair of {my original ...
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33 views

data retrieval vs modeling

i don't have a specific mathematical setting for this question. it's rather high level. if you have a bunch of data X for a variable that we want to predict Y, and all we care about is predicting ...
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29 views

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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9 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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1answer
110 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
44 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
108 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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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
37 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
22 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
31 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
98 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
80 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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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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22 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
22 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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15 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
62 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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2answers
29 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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28 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
20 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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228 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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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 ...