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

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2 views

How do we mine associations from sequences?

My data mining problem is a next web page prediction using the existing web data. For that I have a set of frequent sequences which are obtained using cspade algorithm in R. Now I am not sure how to ...
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1answer
8 views

Need a little help understanding K-means++ seeding

I have been working on a project that involves using K-means clustering for generating adaptive palettes from images. I understand the general process of K-means clustering, and I understand the ...
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0answers
11 views

Posterior predictive for Gamma distribution with unknown scale and shape

I have a question that needs clarification. The posterior predictive distribution can be described as the distribution that a new i.i.d. data point $\tilde{x}$ would have, given a set of $N$ existing ...
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0answers
8 views

choice of maximum likelihood over expectation maximisation

Given a probability distribution two common statistical measures are the expectation value and the maximum likelihood (equivalent to mean and mode?). My question is, given a probability distribution ...
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0answers
12 views

density function of bivariate normal with almost singular correlation matrix [on hold]

Let $X$ be a bivariate normal distribution with mean $[0,0]^T$ and covariance matrix \begin{pmatrix} 1&\rho\\ \rho&1 \end{pmatrix} with $\rho<1.$ I am looking for the behaviour of the ...
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1answer
15 views

Distribution of sum of mean squared errors - weighted sum of chi squared distributed variables

Suppose $X,Y$ are independent chi-squared distributed random variables with $m,n$ degrees of freedom, $X \sim \chi^2(m)$ and $Y \sim \chi^2(n)$. What is the distribution of $$ Z = \frac{1}{m} X + ...
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0answers
23 views

Calculate betting odds algorithm book [on hold]

I'm just wondering, is there any book with good explanation of betting odds calculation algo. Good example is, tennis or poker. After each shot, or next opened card, the odds are changing. And I want ...
3
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2answers
54 views

Maximum of Independent Gamma random variables?

Suppose $Y=\max\{X_1, X_2,\dots,X_N\}$ where all $X_i$ are independent and follows gamma distribution. I know that extreme value theory deals with maximum of random variables. Can anybody tell me, ...
3
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1answer
40 views

Variance of a product of Bernoulli with another distribution

This is probably a stupid question, so my apologies if this is too simple. I have a distribution X, now I play the following game: I toss a coin, if it falls on a head, I get nothing, if it falls on ...
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3answers
40 views

Bernoulli trial - why do we multiply probabilities?

We assume Bernoulli trial is a series of $n$ consecutive independent experiments - each can end with success (with probability $p$) or failure (probability $q$ or $1-p$). I know it's the probability ...
1
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0answers
19 views

Confidence interval syntax in frequentist probability [duplicate]

Let $\theta$ be an unknown population characteristic (say average height). A confidence interval written as $P(\hat \theta - \delta < \theta < \hat \theta + \delta) = 1 - \alpha$ makes perfect ...
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1answer
64 views

How to find the normalizing constant for a distribution of unbounded support?

The probability density of a random variable is $$f(x) = ax^2 e^{-kx} ;k\gt0,0\le x\le \infty$$ What is the value of $a$? I understand that first we'll have to take the integral of the function ...
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1answer
62 views

Probability help needed

I have a R data frame (>2000 obs) ...
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0answers
72 views

Show $∫_0^t X(t,s)dB(s)$ is a Gaussian random variable $Y(t)$ [duplicate]

Show that if $X(t)$ is non-random (does not depend on $B(t)$) and is a function of $t$ and $s$ with $\int_0^t X^2(t,s)ds<\infty$, then $\int_0^t X(t,s) dB(s)$ is a Gaussian random variable $Y(t)$. ...
0
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0answers
162 views

Show that $\int_0^t X(t,s) dB(s)$ is a Gaussian random variable $Y(t)$ [on hold]

Show that if $X(t)$ is non-random (does not depend on $B(t)$) and is a function of $t$ and $s$ with $\int_0^t X^2(t,s)ds<\infty$, then $\int_0^t X(t,s) dB(s)$ is a Gaussian random variable $Y(t)$. ...
7
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0answers
38 views

Drawing n intervals uniformly randomly, probability that at least one interval overlaps with all others

Randomly draw $n$ intervals from $[0,1]$, where each end point A,B are selected from the uniform distribution between $[0,1]$. What's the probability that at least one interval overlaps with all ...
2
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2answers
35 views

Check my proof regarding convergence in probability

I got a bit confused during the end of this proof so I am asking for a check. Take $$Y(n) = \begin{cases} 1 &\mbox{with probability} \ 1 -p_n \\ n & \mbox{with probability} \ p_n \end{cases} ...
3
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1answer
226 views

Molecules movement distribution puzzle

Let's say I have blood samples of whiteblood cells ($x$) and viruses ($v$). Space has been discretized in $LL$ spaces. They have a $p_v$ probability of interacting when found in the same space. I want ...
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1answer
29 views

In a normal distribution, what is the z-score that cuts off the bottom 35% of the scores? [on hold]

My professor mentioned using the invnorm function on my calculator, but many websites say that you need a mean and standard deviation to figure out the answer. Anybody have an idea of where I can ...
2
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1answer
39 views

Can you show that $\bar{X}$ is a consistent estimator for $\lambda$ using Tchebysheff's inequality?

This question was taken from a practice exam in my statistics course. Given a random sample $X_1, X_2, ... X_n$ from a Poisson distribution with mean $\lambda$, can you show that $\bar{X}$ is ...
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2answers
25 views

Probability of two different players scoring a goal

Bookmakers quite often price players to score a goal at any point during the game. For example, they may give Ronaldo a 52% chance of scoring a goal in a game, and Messi a 60% chance of scoring a ...
3
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1answer
57 views

Gamma Distribution and Life of Component?

I came across an old exam question as follows: If the life of one computer component (in years) has Gamma distribution with mean $6$ and variance $18$, how can we find the probability that this ...
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1answer
28 views

Resampling probability

I have a population of n unique items and am taking a sample of r. I am sampling with replacement. I would like to calculate the probability of sampling any specific item x times give the sample size ...
2
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1answer
15 views

Hypothesis Test on Contest, a problems?

We have a contest 1 weeks ago. One question is a bit strange for us as follows: $X\sim B(4,p). $ for test $H_0:p=0.2$ versus $H_1:p>0.2$. if $X=4$, $H_0$ assumption is rejected. calculate ...
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0answers
20 views

Relationship between Poisson and Exponential distribution problem

I'm struggling to understand why I can't use an exponential distribution to solve this question: Astronomers treat the number of stars in a given volume of space as a Poisson random variable. On ...
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0answers
19 views

statistics question [on hold]

An event planner does research and finds that approximately 2.75% of the people in the area where a large event is being held are pescatarian. Treat the 250 guests expected at the event as a simple ...
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0answers
17 views

transform probability density function [on hold]

I have the numeric values to plot a probability density function....they look like ...
-2
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0answers
30 views

University of London Past Paper help [on hold]

Hey this is my third year trying to pass my stats exam, I simply have a bad block when it comes to statistics and need some help. I'm trying to do a 2014 past paper and so far the only thing i can do ...
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0answers
7 views

relationship between power means and population zscore calculations

Can one use a power mean of the ages in a room to determine the age break down of a room? Let's say you have a room full of people, by using the average age and standard deviation of the age, how do ...
3
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1answer
214 views

How to generate a specific number of random binaries with probablities proportional to given values?

I have such a matrix in an excel sheet. It has 140 cells. I want to generate 20 binaries randomly. However, the probability of generating "1" in each cell is proportional to cell's value. Namely, ...
0
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0answers
13 views

how can I save the survival probability that used to calculate NRI for an indiviual?

I am trying to save the survival probability that used to calculate NRI (i.e. in the survIDINRI package) for an individual. and I wanted to use these probabilities to further analyse what kind of ...
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1answer
42 views

How can we find $Cov(X(s), X(t))$ for a compound poisson process?

If I assume that $X(t)$ is a compound poisson process, how can it be found what $Cov(X(s), X(t))$ is? I have seen this over and over in books, but they only state it as fact. It is stated to be ...
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2answers
36 views

Expected number of trials

Consider independent trials, each of which is a success with probability p and derive the expected number of trials needed to obtain k consecutive successes by (a)conditioning on the time of the ...
1
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1answer
36 views

Uniform with dependent parameters

I was helping a student with a question I couldn't solve. We have the following process: X is sampled from a $U(0,1)$ distribution. Then Y is sampled from a $U(-x,x)$ distribution. Therefore I have ...
3
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1answer
54 views

PyMC3 Implementation of Probabilistic Matrix Factorization (PMF): MAP produces all 0s

I've started working with pymc3 over the past few days, and after getting a feel for the basics, I've tried implementing the Probabilistic Matrix Factorization model. For validation, I use a subset ...
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0answers
38 views

CDF of sum of 3 independent discrete uniform random variables on {1,2,…,n}

What is an approximate closed formula for this probability, with a derivation: p(k,n) is the probability, that among $n$ PC discs and $k$ errors in sum on them, there will be at least $1$ disc ...
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0answers
31 views

Conditional Probability [closed]

Let $X_1,X_2,X_3$ be a sample of size $3$ from the Bernoulli distribution . Consider the statistic $S=s(X_1+X_2+X_3)$ . To show that $S$ is sufficient statistic , it is written that ...
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0answers
18 views

Bad regression predictions with probability values

I have to pull through a regression on a set of probabilities (so values between 0 and 1). Those probabilities are related to a binary variable, which I have to forecast exactly. My code basically ...
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0answers
24 views

linear regression and plausibility of forecast

Does there exist any mathematical model where the plausibility for a forecast of the dependent variable by linear regression could be expressed. E.g. in terms of any laboratory parameter measured and ...
2
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1answer
126 views

Deriving Density Function (pdf) from Distribution Function (cdf)

A random variable $V$ has the distribution function: $$ F(v) = \begin{cases} 0, & \text{for $v<0$ } \\ 1-(1-v)^A, & \text{for $0\le v\le1$ } \\ 1,& \text{for $v>1$ } \\ \end{cases} ...
3
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1answer
46 views

What allows us to write $P(T_2 >t) = E[P(T_2 >t)| T_1] $

I am currently working with a time process, $T_1, T_2, ..$. I saw in an associated paper that $P(T_2 >t) = E[P(T_2 >t)| T_1]$. I wasn't sure what property allowed me to do this as it appears ...
3
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1answer
44 views

Significance of $1$ in the model: $Y_i=1[B_0+B_1X_i\geq \epsilon_i]$ in Binary Choice Model?

I'm having a bit of trouble understanding exactly why there is a "1" in the general simple Binary Choice Model where $Y_i$ can take a value of either $0$ or $1$. We also assume that the conditional ...
1
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0answers
38 views

Question about the departure process of a M/GI/$\infty$ queue

Consider an $M/GI/ \infty $ queue with the following service time distribution: the service time is $1/\mu_i$ with probabbility $p_i$, and $\sum_{i=1}^kp_i=1$ and $\sum_{i=1}^kp_i/\mu_i=1/\mu$. In ...
2
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0answers
22 views

EM algorithm: With prior vs. not prior

I have a working EM algorithm without prior. I am asking for some advice on how to add prior on latent variables. Define: $t_i \in \{ +1, -1 \} $: variables of interest to be predicted $p_j \in ...
0
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0answers
13 views

What is inference, training and testing in Undirected Graphical Model? [on hold]

I have a Undirected Graphical Model (UGM) - $ \sum_i w_i\phi_i $ . What is the inference and training here? Suppose I have a train data and test data how do I train and test using this data and UGM? ...
5
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1answer
46 views

Closed form for $\mathbb{E}[\ln (1-p)]$, for $p \sim Beta(\alpha, \beta)$

We know that if $p \sim Beta(\alpha, \beta)$, then $$ \mathbb{E}[\ln p] = \psi(\alpha) - \psi(\alpha + \beta) $$ where $\psi(.)$ is the Digamma function. Is there an easy form for $ \mathbb{E}[\ln ...
0
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0answers
28 views

SVM output to probabilistic affiliation

How can I convert the svm output for multiple class classification(one vs one approach) to probabilistic values? Meaning that I want to have a probability for a tested element to be in each available ...
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1answer
43 views

Help with HW questions

I have two following questions I could not really decipher how to get the P-Value. Data from a recent year showed that 71% of the tens of thousands of applicants to a certain program were accepted. ...
3
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0answers
41 views

By how much the mean and variance in size of beans changes after sampling with replacement?

You have a bag of $n$ beans of different sizes. The mean and standard deviation of the size of these beans is $\mu_1$ and $\sigma_1$ respectively. The probability of drawing a bean is an increasing ...
0
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1answer
348 views

Why probability distribution function gives “~.40” probability when it should have been 1.0? [duplicate]

I am following code given here- http://www.bigdataexaminer.com/how-to-implement-these-5-powerful-probability-distributions-in-python/ Under "Normal Distribution" section, the graph peaks at .40 when ...