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

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How to show that a distribution is poisson distribution?

If n grains of wheat are scattered in a haphazard manner over a surface of S units of area, show that the probability that A units of area will contain r grains of wheat is P = ...
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1answer
22 views

pmf of random variable

There is a random variable that can take 3 values with the following probabilities: Pr(x=0) = 0.4 Pr(x=0.5) = 0.2 Pr(x=1)=0.4 How should i write the pmf of this ...
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19 views

Probability distribution of three random variables

The following formula is a formula I got from a paper that deals with wireless networks specifically when calculating coverage probabilities - if needed I can provide the reference- it is powerful ...
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23 views

Steps: How to derive Probability density function for geometric functions

I am not from Mathematics background and hence lack awareness of many basic knowledge. So, please pardon if this sounds too trivial. I would like to know the steps with which I can obtain the pdf of ...
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0answers
33 views

Cox discrete time regression model question

Cox's 1972 publication Regression Models and Life Tables links logistic regression to an extension of the discrete time proportional hazard model. I do not understand how Equation (21) in the ...
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0answers
18 views

PDF of the largest observation in a sample [duplicate]

Intro Let $P(X=x)$ be a Probability Density Function (PDF). Assume we were to perform $n$ observations from a population that is distributed according to $P(X=x)$ (sample size = $n$). I would expect ...
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2answers
80 views

Transformation Chi-squared to Normal distribution

The relationship between the standard normal and the chi-squared distributions is well known. I was wondering though, is there a transformation that can lead from a $\chi^2 (1)$ back to a standard ...
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0answers
41 views

Probability of event happening after the last event

My question seems to be very trivial, but I'm still stuck with it. It's about probability calculations. Suppose you have a number of people that take a glass of water (event), time between 2 events is ...
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1answer
50 views

Negative Binomial Distribution R

This question was given in class and I was wondering how to do this in R: "Sixty percent of a large lot of old spark plugs are still usable, and they can be individually tested to determine this. Let ...
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3answers
61 views

Regression function of “non-regressible” data

I have some background in probability, and now trying to understand statistics, which sometimes leads to the questions of the following kind. Let $X$ and $Y$ be two random variables that represent the ...
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0answers
33 views

Does Hoeffding's inequality apply to sampling from finite populations?

Based on Hoeffding's theorem, one could easily find the minimum number of samples required for the inequality $\Pr \left(|\bar{X} - \mathrm{E} [\bar{X}]| \geq t \right) \leq \delta$ to hold as ...
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23 views

Calculate probability of consecutive event from R simulations

he problem is to calculate the PMF of consecutive flips of head (M) in N number of coin flips. Consecutive heads, k=0, 1, 2,...,N, the PMF is P(M=k). I use $sample(0:1,N,rep=T,prob=(0.25,0.75))$ to ...
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1answer
32 views

Calculate probability of consecutive event from R simulations

The problem is to calculate the PMF of consecutive flips of head (M) in N number of coin flips. Consecutive heads, k=0, 1, 2,...,N, the PMF is P(M=k). I use ...
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0answers
17 views

How to calculate confidence limits for various scenarios when drawing random cards from a pack?

I'm designing an experiment that involves a subject attempting to determine various attributes of a playing card drawn at random from a standard 52 card pack. The experiment is in four phases: ...
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1answer
13 views

Picking 3 coins from 6 coins without replacement. What is probability of getting a nickel on a certain pick?

I'm having trouble with this problem: There is 1 nickel, 2 dimes, and 3 quarters in a cup. You pick 3, one at a time, without replacement. What is the probability of getting a nickel on the first ...
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3answers
258 views

Uniform random variable as sum of two random variables

Taken from Grimmet and Stirzaker: Show that it cannot be the case that $U=X+Y$ where $U$ is uniformly distributed on [0,1] and $X$ and $Y$ are independent and identically distributed. You should not ...
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0answers
23 views

Sampling from a multivariate distribution

Given $X = [X_1 X_2 \ldots X_n]^{\top}$ is a vector of independent bernoulli random variables and $A \in \{0, 1\}^{m \times n}$ is an arbitrary boolean matrix. Define a random variable $Y$ as $$Y = ...
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1answer
33 views

Need direction in regards to probability based random value generation

I have a daily stream discharge data set spanning 10 years whose histogram looks like this: I would like to use it to set the distribution for a randomly chosen discharge for a given timestep. That ...
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1answer
192 views

Area within a given number of standard deviations from given mean

I have a variable with mean value of 18.85 and standard deviation of 1.45. I want to define the area that is covered by 1.45 standard deviations left and 1.45 standard deviations on the right side ...
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0answers
32 views

How to estimate the correlated individual components from a sum, for a random process?

Assume that there are $N$ realisations of five individual, random variables$X_1$, $X_2$, $X_3$, $X_4$ and $X_5$, which in general could be correlated. We define another random variable ...
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0answers
28 views

Formula the conditional probability of marbles [closed]

I have a interesting question that need your help. I have two sets A and B. Set A have 10 marbles that numbered from 1 to 10. Set B have 6 marbles that numbered from 1 to 6. Randomly choose $g$ ...
5
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1answer
118 views

How to calculate $P (|X − Y | ≤ 1/6)$? [duplicate]

$f_{X,Y} \left( x, y \right) = 1\quad \text{for}\quad 0≤x≤1,\ 0≤y≤1 $ and $0$ otherwise. How to calculate $P \left( |X − Y | ≤ 1/6 \right)$?
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2answers
56 views

Gibbs Sampling and Probability Notation

Problem 1 I am trying to implement Gibbs Sampling for the following problem: There is a grid measuring 3 x 3 sites, each "site" can be designated in a state, $X$, of 1 or -1. The sites are numbered ...
5
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1answer
123 views

Probability of getting the correct direction, given you get the same answer

A town is composed of $2/5$ out of town couples and $3/5$ in town couples. If a couple is from out of town, the probability that the husband and wife will give you the correct directions ...
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39 views

Rate of convergence of the coverage probability of bootstrap confidence intervals

I was wondering if someone knows good books or references that deal with this subject : "The rate of convergence of the coverage probability of bootstrap confidence intervals" Many thanks for your ...
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22 views

My naive bayes classifier doesn't show probabilities [duplicate]

I'm trying to predict the probability between 1-0 and have found that naive bayes is supposed to show this, however when I use it I only have ...
2
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1answer
74 views

How to estimate the individual components from a sum for a random process?

We have $N$ realisations of five individual, IID random variables $X_1$, $X_2$, $X_3$, $X_4$ and $X_5$. We define another random variable $S = X_1+X_2+X_3+X_4+X_5$. Now, for a given $S$ generated from ...
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30 views

Trying to find a classifier that will give me probability predictions between 0-1 in weka

This is the first time I've done any sort of predictive modelling and I think I've really confused myself. I have a training set of data with a column at the end that has either a 1 or a 0 in it. ...
2
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1answer
41 views

What sampling method will be suitable when there is no published list is available?

As there is no published list of population (employees), how can I select my sample? Even if I want I can not go for judgmental sampling as the academicians in my University strongly disagree for ...
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1answer
86 views

What are some good references on how probability theory got mathematically rigorous?

I am working on a term paper for an analysis course and I thought it would be interesting to talk about the connection between analysis and probability theory. Honestly, it would also benefit me a lot ...
2
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1answer
24 views

Combination/permutations question where repetition is allowed

So I guess this is a combination/permutations question where repetition is allowed. What is the % chance that six six-sided dice will show at least 3 duplicates of the same number or that there will ...
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15 views

Conditional and joint pmf of sequences of random variables

I have random variables $X_1...X_N$ which are Poisson($\theta$) distributed. I also have inclusion indicators $Y_1...Y_N$ which are Bernoulli($\pi$) distributed. These indicate whether $X_i$ is ...
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1answer
58 views

What is the probability that a girl is taller than a boy, with boys ~N(68, 4.5) and girls ~N(62, 3.2)?

"Given that boys' heights are distributed normally $\mathcal{N}(68$ inches, $4.5$ inches$)$ and girls are distributed $\mathcal{N}(62$ inches, $3.2$ inches$)$, what is the probability that a girl ...
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1answer
19 views

joint probability distribution with a constant

If $X \sim N(0,1)$, then what is the joint probability distribution of $(X+1,X)$? An attempt: $f(x,x+1)=f(x|x+1)f(x+1)=f(x+1)$, so $N((0,0),(0,0;0,1))$. Note sure though...
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2 views

Softmax factorization for a hidden markov model

I'm trying to formulate a hidden markov model where the transition and emission probabilities are governed by a softmax distribution. I'm not sure if this is a good idea, but I thought it could be ...
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1answer
38 views

Conflicting formulae to determine the probability that an event has occurred

Assume a molecule that at each time step has a probability $p$ of being removed from the body. After one time step, it seems to me that these probabilities exist: Molecule still in body: $1 - p$ ...
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0answers
21 views

Can the law of total covariance apply to variables from different sample spaces?

Wikipedia says this about the law of total covariance (http://en.wikipedia.org/wiki/Law_of_total_covariance): In probability theory, the law of total covariance,[1] covariance decomposition ...
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24 views

how to test for significant preference with two variables with different number of outcomes?

In a random choice trial with two parameters (color and location), I want to test whether a choice is influenced / driven by one other factor or the other, or whether they are independent. In detail: ...
2
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1answer
93 views

Convergence of $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$ if $X_1, \dotsc , X_n \sim U(0,1)$

$X_1,X_2,\dotsc ,X_n$ are independent, uniformly distributed random variables on the interval $[0,1]$ The question is the convergence of the sequence: $X_{{\lfloor n/3 \rfloor}}^ \space\small{(n)}$. ...
2
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1answer
44 views

What's the statistical method where you add a certain number to each sample to make the distribution slightly more uniform?

Please forgive my lack of knowledge - it's been a while since I've taken classes in statistics, and even then, it was not my strong point. I'm trying to recall a method used to upweight all values in ...
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0answers
15 views

How to estimate Extreme value distribution parameter

Assume that I have non-negative Gamma random variables $\{X_i,i=1\dots n\}$ and I want to find $M_n=\max\{ X_i\}$. I want to apply generalized extreme value distribution (GEV), but how to find $\mu$, ...
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0answers
6 views

comparing probability of imbalance classes

I am trying to figure out what id the standard way to compare the probability of occurrence of two imbalances classes: let say there 1500 web pages with different languages edition (e.g. Wikipedia). ...
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0answers
14 views

Iteratively re-weighted least squares

I am a frequent user of Emblem and I am trying to develop my understanding of the modelling process by understanding how exactly Emblem fits the models. To achieve this I have taken a very simple ...
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23 views

Calculating the probability of both teams to score in a soccer match?

New to the forum, and while not quite an idiot, I have no where near the knowledge and nous of all in here. Consider the following scenario: Soccer match Home team - Team A Away team - Team B ...
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1answer
38 views

Does the “joint probability” of two events take their order into account?

When we speak of "joint probabilities" in a general sense, do they take the order in which the events occur into account? Or alternatively, is it -by defnition- true that $P(A\cap B) = P(B\cap A)$ ? ...
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1answer
25 views

What is the values of the $P(a)$ and $P(b)$ here?

I am watching a video on EM algorithm here. It gives an example of how EM algorithm works. At first two Gaussian distributions are randomly given, and then by iterative calculations their parameters ...
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1answer
85 views

Random variables with some properties (conditional expectation)

I am looking for two random variables which fulfills the following two things: a) $\mathbb E(X|Y)<\infty$ and $\mathbb E(Y|X)<\infty$ b) $E(X|Y)> Y$ and $\mathbb E(Y|X)>X$ a.s Here is ...
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1answer
72 views

which distribution should be used in this question?

A basketball player succeeds in making a basket three tries out of four. How many times must he try for a basket in order to have greater than 0.99 probability of making at least one basket? In this ...
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15 views

Meta analysis, joint posterior distribution of study effect

Meta analysis (with common study variation $\sigma$) often assumes that: $$ X_{i,j} | \theta_i \overset{ind}{\sim} N(\theta_i,\sigma)\\ \theta_i \overset{i.i.d.}{\sim} N(\mu,\tau) $$ where ...
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1answer
28 views

Basic summation of conditional probabilities question

I read on Bishop Chap8 P 374 that: sum(P(b|c)P(c|a)) = P(b|a) where the sum is over c. Can you prove that?