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

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Bayesian Updating Process, 3 signals and 2 states of the world

Suppose Nature chooses a state $\omega = \{X,Y\}$ at $t=0$. Long-lived agents observe a signal $s_t$ at every period $t$, where $s_t = \{ x,y,z \}$. Agents all hold a common prior $\mu_0 \in (0,1)$ ...
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24 views

can we generate a random words from english latters that follow the bigram of english language

the main issue is that several research building their solution of detecting and classifying English language is based on bigram distribution. however, I would like to know if it possible to generate ...
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13 views

Probablity calculation for at-least clause case

I saw the question: What is the probability of 1 out of 5 randomly selected people agree with the statement that men having more right for job compare to women? ...
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1answer
23 views

Can an a.s. (almost surely) finite random variable be a.s. UNbounded?

I thought that if a random variable, $\eta^2$, is assumed to be a.s. finite, then $\eta^2$ must be a.s. bounded. In the Martingale Central Limit Theorem in Hall & Heyde, they assume this: "let ...
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1answer
19 views

Chi-Squared Goodness of Fit Test Alternative? - Zero Can't Be in Denominator

I have 5 zones(categories) in which a certain percentage of total sinkholes exist. I have 5 different maps that I am testing to see which one provides me with the best fit to my expected percentages ...
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2answers
57 views

What probability distribution best describes my data?

I have a variable whose values are summated scale scores with values ranging from 3 to 21. I considered this variable as a scale variable (though with restricted range). In order to model the relation ...
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1answer
100 views

maximum-likelihood of a sequence of events described by a Bernoulli distribution

I am having quite some troubles with the following homework: In a city it's measured for the whole year whether it rained or not. A distribution $\textrm{Bernoulli}(r_t|\rho)$ characterizes the ...
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1answer
24 views

Probability conditions [on hold]

We have four coins (10 Cent, 10 Cent, 50 Cent, 50 Cent) and choose randomly two of them. The sum of the two coins is a random variable X. i) Show that the probability for X to be 20, 60, 100 is 1/6 , ...
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2answers
64 views

Bias in jury selection?

A friend is representing a client on appeal, after a criminal trial in which it appears that jury selection was racially biased. The jury pool consisted of 30 people, in 4 racial groups. The ...
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16 views

How to compare the distances or divergence between two groups of datasets

If I have two groups of data sets. Each group has two arrays of empirical data. In the first group each array has, say, 50,000 data points, and in the second group each array has 3,000 data points. ...
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1answer
43 views

Moment Generating Function of a nonlinear transformation of an exponential random variable

Let $\tau$ be an exponential random variable, with parameter $\lambda$. Let $$ V = \delta^\tau $$ where $0 < \delta <1$. Sorry if this notation seems strange, but it is what I am using, I ...
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1answer
32 views

How can I determine source type of a sequence?

I have sequences of binary events, e.g. $s=0001101$. I know that there are two types of sources $A,B$ possible generating each sequence. There are different conditional probabilities for a hit given a ...
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12 views

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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0answers
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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0answers
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
99 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
51 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
32 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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2answers
113 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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49 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
51 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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25 views

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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30 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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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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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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80 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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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
60 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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37 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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117 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
45 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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17 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
41 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
23 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\ ...