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

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Relationship between Gaussian mixture model probability and $\text{L}^2$ norm?

My question is: what are the differences between the various scores for a data set modeled with a Gaussian Mixture Model (GMM)?. When evaluating the probability of set of points $D$ under a GMM we use ...
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25 views
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The probability of m out of K things being wrong with an error of ɛ

I have a homework question about a machine-learning algorithm that uses ensemble learning with simple majority voting. Assuming we have K hypotheses, each with an error ɛ, the question asks us to ...
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1answer
50 views

Which distribution to use for a probability problem?

In a food processing plant, on average, 2 packaging machines breakdown per week. I let x be the number of processing machine breakdowns in a week. So x is Poisson(2), but one part of the question ...
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16 views

QQ plot in Python

I generated a qq plot using the following code. I know that qq plot is used to check whether the data is distributed normally or not. My question is what do the x and y axis labels indicate in qq plot ...
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33 views

How to do inference over two steps in a graphical model simultaneously?

Here is my problem: I have observed data $D$ about a physical object described by $M$. I would like to determine the posterior distribution of $M$ given $D$, or $p(M|D)$. Now I can't infer this ...
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21 views

A or B but not Both - Can't figure it out

According to a survey in one U.S. city, 49% of women between the ages and 25 of 35 are married, 47% are working full time, and 21% are married and working full time. If a woman between the ages of 25 ...
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2answers
223 views

Why doesn't my Wiener process simulation work?

The Wiener process at time $t=0$ is $0$. It has independent increments, so $W_t-W_0 \sim N(0,t-0)$, but wouldn't it mean that $W_t\sim N(0,t)$ for every $t$? But if I try to simulate a a ...
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1answer
16 views

Temporal correlation [on hold]

I have three events, temporal happpening in t1, t2 and t3. I have a master event, that happens in t0. Being ...
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17 views

On conditional/joint probability [duplicate]

Problem 1 The table on the left shows the joint probability distribution between two random variables - X and Y; and the table on the right shows the joint probability distribution between two random ...
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17 views

Uniform Convergence of Moment under Empirical distribution

Let $X$ be standard Gaussian random variable with cdf $F(x)$. Let $\{X_i\}_{i=1}^n$ be a sequence of i.i.d. standard Gaussian random variables. And let $F_n(x)=\frac{1}{n}\sum_{i=1}^n1_{\{X_i\leq ...
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1answer
46 views

Upper Bound on $E[\frac{1}{1-X}]$ where $E[X]=a$ and $0<a<1$

$X$ is a discrete random variable that can take values from $(0,1)$. Since $\varphi(x)=1/x$ is a convex function, we can use Jensen's inequality to derive a lower bound: $$ ...
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8 views

How do you normalise in a sequential bayesian aproach

Lets say you have an event G that a defendant is guilty, and you have variable F probability of finding his footprint at a crime scene assume you have the following information beforehand: so you ...
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2answers
65 views

Probability of rolling one die by two persons 3 times each, and problem with pulling out cards

So suppose you have one die. Person A rolls one die 3 times. Person B does the same after A is finished. What is the probability that person A's smallest number (of his/hers 3 rolls) is greater than ...
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32 views

compare muliptle probabilities

I have built three decision tree model to predict the response for three offers (One model per offer). I want to find the best offer for each customer based on the predicted probabilities. All offers ...
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8answers
2k views

Random walk on the edges of a cube

An ant is placed in a corner of a cube and cannot move. A spider starts from the opposite corner, and can move along the cube's edges in any direction $(x,y,z)$ with equal probability $1/3$. On ...
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4 views

Dependence of PDF of LLR of symbols

I have a system model with $y=hs+\sum_i^n gx+n$ where h is rayleigh fading desired channel, g is interfering channel x is interfering symbols. $\hat{s}=w*y$ where w is MMSE filter. On what factor pdf ...
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1answer
25 views

A quiz problem on normal distribution and probability?

I was asked this question in interview. I couldnt answer this, can some one help. An investment, 16% chance to lose money on a quarter, and each quarter follows i.i.d. normal distribution. �Q: what ...
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conditional distribution question

I have a joint distribution which factorizes as follows: $$ P(y, w, \beta) = P(y|\beta, w) P(w) P(\beta) $$ Now, I want to write the conditional distribution for $P(w|y, \beta)$, so this should be ...
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2answers
33 views

data are drawn from a probability distribution P?

what does it mean to say data are drawn from a probability distribution P?
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2answers
36 views

Systematic Sampling with unequal probabilities

I found the library Sampling in R to conduct a systematic random sampling with unequal probabilities. I got my sample but I really don't know how that sample is selected. Is there anyone that can ...
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1answer
51 views

pdf of the square of the sum of Nakagami random variables

I am trying to find the probability distribution function (pdf) of the following $$Y=\big|\sum_i X_i\big|^2=\big|\sum_{i\leq 2} h_i \, a_i\big|^2 $$ with $$h_i\sim \text{iid} ...
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3answers
58 views

Dependent or Independent…a little intuition

I have a time series that describe the power consumption of a building. For every hour of the day I have a measurement (e.g Hour 0 = 2.3 kWh, Hour 1 = 4.2 kWh etc). Do you believe that the ...
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1answer
40 views

basic question about machine learning and probabilistic framework?

Why do we assume that the pair (X,Y) where X and Y are features and labels respectively are random variables governed by a probability distribution? Why does this assumption make sense? What if the ...
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12 views

signal with equally likely probability

The input to the system is x(n)=1 or -1 with equally likely probability. Can I conclude that x(n) is dirac impulse function => X(Z)=1
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1answer
36 views

Nonlinear things that one can do to a probability density function

Say $f(x)$ is a smooth probability density function on $\mathbb{R}^n$ with compact support region. This wikipedia page http://en.wikipedia.org/wiki/Maximum_entropy_probability_distribution explains ...
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28 views

How to find P(X = Min(X,Y)) for an exponentially distributed function?

Assuming $X$ and $Y$ are independent, and each of them have their own parameters $A$ and $B$, how do I find $P(X = \min(X,Y))$ for an exponentially distributed function? I understand that ...
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1answer
21 views

conditional probability, change of variable and Jacobean

I have a question, and I am guessing that the question arises due to my lack of good understanding in the change of variable technique. I would like to evaluate $f_X(x)$. When $f_Y(y)$ exists, I can ...
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1answer
35 views

Divergent sequence of random variables with expected value zero

I am trying to think of a sequence of random variables $X_n$ such that $X_n\rightarrow\infty$ as $n\rightarrow \infty$ but $E(X_n)\rightarrow0$. Can you please show me some examples?
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13 views

Joint Probability of multiple correlated variables

I have annual extreme values (logIII distribution) from multiple (3 in this case, but looking for a solution that is more universal) sites, and I am trying to calculate the probability that all exceed ...
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1answer
21 views

Convergence of Sum of Sums of random variables : trivial?

I have a sequence of i.i.d random varaibles $X_1, X_2, ...$ with finite mean $\mu$ and finite variance. I also have another sequence of i.i.d random varaibles $Y_1, Y_2, ...$ with the same finite mean ...
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0answers
8 views

Convert data to TS variable in AR [on hold]

How can I convert my data to time series data in R? Firstly cpi <- read.table("y.txt", skip = 1, col.names = c("Time", "CPI")) Thanks
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1answer
45 views

Conditional probability and frequentism

I'm brushing up on my basic statistics from undergrad engineering, and (being much older) I've found myself trying to understand the Frequentism vs. Bayesianism debate. Luckily there's plenty online ...
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Poisson Probability question 3 [on hold]

The National Safety Council (NSC) estimates that off-the-job accidents cost U.S. businesses almost $200 billion annually in lost productivity. Based on NSC estimates, companies with 50 employees are ...
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31 views

How do I classify data with multiple dimensions using a gaussian classifier? [closed]

I've computed the equation inside the brackets (but not i): Features=dimensions (x,y)..R^n Ck being the covariance matrix, z being the input vector, u being the mean vector, N being the number of ...
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1answer
39 views

Example of probability rule

Can someone provide me with an example (real life example, if possible) in which $P(a \cap b) < P(a) \times P(b)$?
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17 views

How to determine certainty on a range of probabilites and overall accuracy?

I'm trying to determine if the prediction made by my classifier is certain enough. Known: The probabilities for each possible class, for example: ...
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1answer
18 views

How to compare two Bayesian networks?

I have two different datasets on which I've applied the same learning (K2) algorithm to learn a Bayesian network. I have the conditional probability table (CPT) of the class variable, for each of the ...
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14 views

Method for ranges of increasing numbers to determine representative number

The good people on the R site suggested I ask my question here. I seek guidance on R code to make a probability calculation based on survey data. The survey asked respondents to select from five ...
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192 views

Elementary counting arguments: Family with 6 children, gender and birth

Problem 2.1.5 from Basic Concepts of Probability and Statistics, 2nd Ed. by Hodges and Lehmann Suppose you know that a family has 6 children, 2 boys and 4 girls, but you don't know their sexes ...
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116 views

logistic regression prediction: changing interpretation with changing prior

The data include 3 equally sized subsets A, B and C, belonging to two classes: A belongs to class 1. B and C belong to class 2. The prior probabilities of an observation coming from class 1 ...
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Nearest Neighbors and Voronoi Volumes in High-Dimensional Point Processes

Tessellations of space for a given set of points into non-overlapping cells play an important role in the fields of science on form and stochastic geometry. Among many possibilities of tessellations, ...
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1answer
51 views

finding upper bound for $P(T=0)$

Let $X_1,X_2,...,X_n$ is a random sample of Poisson distribution with parameter one. if $T=\bar{X}(n-\bar{X})$ how can find upper bound for $P(T=0)$
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1answer
40 views

On an implication of the memoryless property of the exponential random variable

I know that if we take $X \sim Exp(k)$ then we have this property: $$P(X \ge s + t | X \ge s) = P(X \ge t)$$ But why does this imply that $X | X > x$ has the same distribution of $X$ only ...
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1answer
62 views

What is usually meant when it's said humans are bad at probability? [closed]

Perhaps this is outside the scope of CrossValidated, but I don't think just one thing is meant by the oft-said claim that "our brains are bad at grasping probability," or the like. What would you say ...
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19 views

decomposing distribution function of sum

I am thinking about decomposing distribution function of sum of two random variables into sum of distribution function. Let assume $Y_1\sim F_1$ and $Y_2 \sim F_2$ and $Y_2\in \mathbb{R}$ and ...
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1answer
15 views

Posterior probability of an image when the posterior of local features are known

Lets assume the local features $x_1, x_2, \dots x_n$ of an image $I$ are independent. I know if $p(x_i|c)$ are given $p(I|c)$ can be defined by $\prod_{i=1}^N x_i$ But I dont know how to calculate ...
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92 views

Cluster prediction of incoming time series(partial)

I have a data set (24 x 1000) (hour x kwh) which contains 1000 time series of a buildings' power consumption, measured every hour. After applying k-means clustering using the dtw criterion I create 5 ...
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36 views

MLE of a linear function

So I have a function $$f(x\mid\theta) = \frac{1+x\theta}{2}$$ For the interval $-1\leq x\leq 1$. I need to find the mle of $\theta$ but the only way I've learned how is to take the derivative which ...
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1answer
46 views

When to use empirical cdf?

I saw in some papers that people sometimes use empirical cdf or complementary cdf to quantify the distribution of data. What is the advantage of using them and what interesting can they tell about ...