Tagged Questions

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

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0answers
10 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 ...
0
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0answers
23 views

Stochastic measuring of Poisson process

Railroad cars' lengths are distributed by $exp(\lambda)$. The train has n cars. We're standing $t$ length units from the beginning of the train, and we are measuring the car's length. What is the ...
0
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0answers
20 views

Formula the conditional probability of marbles [on hold]

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 $g$ ...
4
votes
1answer
111 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 $P \left( |X − Y | ≤ 1/6 \right)$?
3
votes
2answers
50 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
votes
1answer
120 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 ...
0
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0answers
35 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 ...
-1
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0answers
21 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
64 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 ...
0
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0answers
28 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
votes
1answer
40 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 ...
6
votes
1answer
75 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
votes
1answer
20 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 ...
1
vote
0answers
13 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 ...
1
vote
1answer
54 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 ...
0
votes
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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0answers
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 ...
4
votes
1answer
37 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: $1 - p$ ...
2
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0answers
20 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 ...
0
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0answers
16 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
votes
1answer
87 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
votes
1answer
40 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 ...
0
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0answers
14 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 $\mu$, ...
0
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0answers
4 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). ...
0
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0answers
13 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 ...
1
vote
0answers
19 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 ...
0
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0answers
17 views

How normalize this distribution probabilities [closed]

I have these probability distributions, how can I normalize then calculating the Kullback Leibler divergence ? ...
2
votes
1answer
36 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 $P(A\cap B) = P(B\cap A)$ ? ...
0
votes
1answer
24 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 ...
0
votes
0answers
17 views

Confidence interval and probability mixed [closed]

An advertising agency needs to create a television advertisement for a sun block. The hirer, who makes this product, says that 40% of customers prefers his/her brand. The agency did a survey to verify ...
6
votes
1answer
84 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 ...
0
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1answer
71 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 ...
0
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0answers
13 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 ...
0
votes
1answer
26 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?
7
votes
2answers
617 views

Why does convolution work?

So I know that if we want to find the probability distribution of a sum of independent random variables $X + Y$, we can compute it from the probability distributions of $X$ and $Y$, by saying $$f_{X ...
0
votes
0answers
39 views

How to determine the pdf from the sum of different distributions

Consider a discrete random variable $Z(t) = \phi_1Z(t-1) + \phi_2Z(t-2) +\dots+\phi_pZ(t-p) + \mu(t)$ $Y(t) = Z(t) + \eta(t)$ where $\mu$ is a zero-mean deterministic nonlinear signal following a ...
0
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0answers
22 views

Beta Binomial Distribution with a priori $\alpha$ and $\beta$ to Account for Probability Forecasts

I am trying to use a beta binomial distribution to calculate how much a single vote would count in a 2-choice election, given $n$ voters and a $p$ forecast: $ f(\lceil\frac{n}{2}\rceil;n,p) $ where $ ...
1
vote
1answer
34 views

nonparametric method to calculate the probability how alike two samples are

I have two samples with each couple of hunderd observations. I want to calculate a probabilty how much they look alike. I'm aware of tests like kolmogorov smirnov but I don't think I need this. I ...
-1
votes
1answer
51 views

Indepent variables and these functions [closed]

Random variables $x_1, x_2,...,x_n$ are independent. Then I want to show whether these functions $$y_1=f_1(x) \\ y_2=f_2(x) \\ ... \\ y_n=f_n(x)$$ are independent or not . How to prove this?
0
votes
1answer
21 views

Asking for help with a probability question for “learning dyadic data”

I am reading a paper "Learning from dyadic data" written by Thomas Hofmann, Jan Puzicha and Michael I. Jordan, which lays a foundation for a later paper that proposes the famous probabilistic latent ...
2
votes
0answers
40 views

joint distribution, probability, calculating probabilities under false independent assumption, when the random variables are actually dependent

Suppose I have random variables $X,Y,Z$ and I would like to compute the probability that random variable $X$ is smaller than $Y$ and $Z$: $$ \pi_X \overset{def}{=} Pr(X < Y, X < Z) = \int Pr(x ...
0
votes
0answers
16 views

The probability density function using the Laplace transform

I am reading a paper that is trying to derive the following probability $$ \mathbb{P} \biggl( F \geq T(I+W) \biggl)$$ Assumptions: 1- Assume that the $F$ has a finite first moment and admits a ...
0
votes
0answers
19 views

Interesting question about full rank of random matrix

I have a question about rank of a random binary matrix. Assume that I have to make a random binary matrix with its size are k rows and n colmuns (k<=n). Each columns only has 1 or 0 values. Now I ...
0
votes
0answers
26 views

How to calculate the probability of various outcomes in a gambling situation

Suppose that the probability of losing a dollar is 2/3 and winning is 1/3. I start with X dollar, what is the probability that I come out with Y dollar? I assume that I go home if I lose all the ...
0
votes
1answer
24 views

combining subjective probability estimates and statistical estimates for forecasting

At the end of the year forecasters usually struggle year to predict landing estimate for the financial year due to variety of reasons including volatility, unreliable demand projections, inventory ...
2
votes
0answers
56 views

Probabilities of odds ratios in random intercept models?

I'm using R and the lme4 package to compute mixed effects models with binary outcome (glmer). I have included continuous ...
0
votes
1answer
34 views

How to compare probabilistic classifiers?

Assume that we have a very long sequence (i.e. a list) of nominal-valued observations. For example: A A C B ... B A B C We have also a corresponding sequence of ...
3
votes
1answer
51 views

Entropy of Sum vs Difference of Random Variable

I am looking for a proof of the following fact Let $X$ and$ X'$ be i.i.d on $\{0,1,2\}$ (not necessarily uniform). Prove that $$H((X + X') \mod3) \leq H((X - X') \mod3)$$ where $H()$ is the ...
2
votes
1answer
16 views

Arbitrary noise generation

lets say I have some noise time series and I want to sample random numbers from the same underlying distribution as this time series. An easy algorithm I have found online is basically you take the ...
1
vote
0answers
6 views

Collision in randomly generated String [duplicate]

I have a function which gives me randomly a combination of letters from A-Z and numbers from 0-9. I want to generate 20000 keys out of this. My question is now that I want to determine the probability ...