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

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22 views

Are all variables random in probability? [on hold]

Probability means what is the likelihood that the given event would occur. Are all variables random in probability ? If so that is probability always talks about stochastic. And if so, Why is ...
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15 views

Looking for Approach: Cost-sensitive analysis based on probabilities and costs that differ per example

I've been struggling with the following problem. I have a logistic regression model that returns probabilities for three classes (A, B, C). The problem is, I need to choose A, B, C or refrain from ...
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41 views

emails arriving in a Poisson process

Emails arrive according to a Poisson process with rate $λ=2/hour$. You check your inbox (instantly reading all new emails) at time $t=5$ hours and also at some uniformly distributed random time ...
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161 views

A practical question in simulating real world outcomes

PredictWise aggregated polling data and, for each state, estimated the probability that the Obama or Romney would win. Here is the polling data. The data frame has 51 rows(51 states). the name of this ...
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0answers
17 views

Electrical components failing in a Poisson process

A machine has infinitely many identical components. They fail according to a Poisson process with rate λ = 4/hour. A repairman arrives at time t and instantly repairs all of the broken components, but ...
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15 views

Indirect inference and p-value estimation

Let there be three continuous predictor variables X1, X2, and X3. Each variable is of length n. The correlation between the variables are rho12, rho13, and rho23. There is a binary outcome variable ...
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2answers
68 views

Probability of finding a point in the unit circle?

Consider the experiment where a pair of numbers (x,y) is chosen at random in the unit square; that is, x and y are uniform (0,1) random variables. What is the probability of (x,y) lying within the ...
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3answers
57 views

Tricky Poisson distribution question

Am new to probability and have been struggling to solve the following question. Assume $X_1, \ldots,X_4$ are IID with $X_i ∼ \text{Po}(λ)$. Let $Y = \frac{1}{4} (X_1 + \ldots + X_4)$. Find ...
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1answer
14 views

Model for probability of N autocorrelated events

Say we have $N$ birds, $r$ is the probability that one bird sings. What is the probability $p$ that any of $N$ birds sings? If we assume independence, there is a simple model describing the ...
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0answers
31 views

Probabilistic score vs $L^2$ norm to evaluate Gaussian Mixture Models

There seems to be (at least) two ways that one could evaluate the fit of a Gaussian Mixture Model (GMM) to a data set. First, a probabilistic score, is the log likelihood of a set of points $D$ ...
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1answer
46 views

What is the reason for this discrepancy between confidence level and probability?

I ran the following R code: library(Hmisc) binconf(x=1, n=70) # PointEst Lower Upper # 0.01428571 0.0007327613 0.07658187 Which is the ...
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12 views

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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2answers
169 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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0answers
23 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 ...
3
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0answers
55 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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27 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
233 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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18 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 ...
2
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0answers
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 ...
5
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1answer
51 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
70 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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0answers
33 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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6 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
28 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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19 views

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
40 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 ...
2
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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
59 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
41 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
38 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 [closed]

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
46 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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27 views

Poisson Probability question 3 [closed]

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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0answers
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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19 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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197 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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133 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 ...