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

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Determining demographics by restaurant visits

Assume Person X likes to visit different restaurants at different times. We would like to determine the current estimate of their demographic distribution based on all prior information we know from ...
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21 views

Chance game algorithm - winning strategy?

I was thinking of a game and its winning strategy for the past week. Say, there is a provably fair machine that spits out numbers from 1 to 10000. As the machine cannot produce true random values, ...
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2answers
104 views

What does $\{x|x = 7\} = \emptyset$ mean? (Probability)

To my understanding $\{x|x = 7\} = \emptyset$ means that the number seven is a not allowed value. But I do not understand the meaning of "$x|x$". Can anybody please explain $\{x|x = 7\} = \emptyset$ ...
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2answers
69 views

Calculating probability mass functions with constraints from cumulative distribution

This is a self-study question. The name of the book is called: Applied Statistics and Probability for Engineers by Montgomery and Runger. This problem is on page 73. It's exercise 3-41. The entire ...
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1answer
75 views

Does the birth date of professional boxers matter? Prove/disprove what an astrologer might predict

As a followup to my question about the birth month of boxers, I am posing the fundamental question along with my hypothesis (testing if there is any truth to a conclusion an astrologer might make): ...
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20 views

Confidence interval of a function of Maximum Likelihood estimates

I know the distribution of $x$. The distribution of $x$ is a function of $Y$ i.e. $P(X=x \space |\space Y)$. I observe one $x_i$ in nature and I want to calculate a confidence interval for the actual ...
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2answers
122 views

Statistical significance of birth month of professional boxers

I looked at the birth dates of the top 100 ranked professional boxers of all time (67 of them to be exact). 40% of them were born during certain 3 month-long time periods. If birth date of boxers ...
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3answers
163 views

Why Normalizing Factor is Required in Bayes Theorem?

Bayes theorem goes $$ P(\textrm{model}|\textrm{data}) = \frac{P(\textrm{model}) \times P(\textrm{data}|\textrm{model})}{P(\textrm{data})} $$ This is all fine. But, I've read somewhere: ...
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1answer
41 views

Determining probability mass function (PMF) using Bayesian approach

For instance, a person is trying to determine the light intensity (unit: Candela) from a source that he knows must be coming from one of the 3 mediums (A, B, and C). From his experience he have ...
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14 views

Polynomial chaos: How to calculate PDF of the response surface analytically?

A response surface in polynomial chaos is represented as; $y(x,\vec{\xi}) = \sum^{N_p}_{i=}c_i (x)\Gamma_i(\xi_1,\xi_2\dots\xi_n)$. But how is the analytical pdf of $y$ calculated? One way to ...
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0answers
25 views

Determining a greater than chance cutoff for an assessment's results

I recently collected a set of data, and before I completed an analysis of it, I wanted to remove any "bogus" entries from participants that didn't actually read the stories. The study I conducted had ...
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1answer
35 views

Exclude Some samples for calculating CDF

I am calculating the asymptotic cumulative distribution of $M_n = \max(X_1,X_2,\dots,X_N)$. My problem is $X_1,X_2,\dots X_p$ and $X_k,X_{k+1},\dots,X_N$ have non identical CDF for $p<<k$ and ...
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66 views

How to calculate probabilities based on cumulative of time series?

I am trying to do predictions on plant growth based on cumulative of time series data. Unfortunately I am not a statistician, just a programmer tasked with writing the application that does this (PHP ...
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0answers
21 views

Transition probability matrix negative values of an M/M/C in R

I am trying to calculate a transition probability matrix of an M/M/C in R. The information given is the following : An IT support help desk represents a queuing system with five assistants taking ...
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1answer
32 views

Independent events in sequence

If I flip a fair coin twice, the probability of at least one Head is 0.75 (HH, HT, TH and TT). I flip the coin once and it lands Tails. In order to get at least one Head, the probability of the ...
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0answers
15 views

MC to estimate coverage probability of bootstrap [on hold]

I am a novice at R-coding but I am trying to use Monte Carlo to estimate the coverage probability of standard normal bootstrap, basic bootstrap, and bootstrap percentile with bias correction. The MC ...
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1answer
29 views

How to use geometric proximity in classification

I am doing a classification of certain regions of an image. Let's say I have done the classification, and some classes have been classified positively (negatively) with high probability. For my ...
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0answers
16 views

Information theory without normalization

I'd like to know if there is a way anyone knows of for doing information theory with unnormalized densities. Specifically, I hav two log likelihoods $\phi(x), \psi(x)$ and so I can write: $p(x) = ...
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0answers
24 views

Families of distributions with bounded variations

For what family of probability distributions $f(x)$ do we have the following property? $$ \forall x, \quad \int f(u) - f(u+x) du \leq L\| x \| $$ for some $L$. Can we say anything about the ...
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1answer
35 views

Independent and Identically Distributed(i.i.d.) Random Variables

The assumption that observations be i.i.d. tends to simplify the underlying mathematics of many statistical methods . However in practical applications of statistical modeling the assumption may or ...
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0answers
18 views

Quadratic model as linear decrease in proportions

Assume $Y_i <= X_i$ for all $i$. The conditional expectation of our data was found to satisfy $E[Y|X=x] = a1*x-a2*x^2$ to very good accuracy for a large range, with $0<a2<a1<1$. ...
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1answer
41 views

What is the expected number of coin flips, if you stop when the first coin flip is the same as the last?

In order to calculate the $\text{E}[X]$ where $X$ is the number of total coin flips, this is the approach I took: The probabilities are: $Pr(H) = p$ $Pr(T) = (1-p)$ Define indicator random ...
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95 views

Probability and Statistics Question [closed]

Hi guys I really need help with this statistics question I'm not really even sure how to start this is, could someone just explain how to do this problem I'm really behind in the class and don't know ...
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22 views

I want prove $E[\int_{\Lambda}h(y)\mathcal M(t,dy)]=t\int_{\Lambda}h(y)\lambda_L(dy)$ and $\dots$

if $\Lambda$ is a Borel set such that $0 \notin \bar \Lambda$ Then. $$E[\int_{\Lambda}h(y)\mathcal M(t,dy)]=t\int_{\Lambda}h(y)\lambda_L(dy)$$ and $$E[(\int_{\Lambda}h(y)\mathcal M(t,dy)-t\int ...
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1answer
23 views

Reparameterization of probability distribution (spike and slab)

I try to understand a statement in this paper: http://papers.nips.cc/paper/4305-spike-and-slab-variational-inference-for-multi-task-and-multiple-kernel-learning.pdf In particular, I am talking about ...
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2answers
40 views

Weakly correlated Random variables

If $N$ random variables are identically distributed but weakly correlated, in what condition we can approximate them as independent identically distributed (iid) ? I saw an old paper where based on ...
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1answer
27 views

If $X^T(t)=X(t\land T)$ is said to be the process $X$ stopped at $T$. I want prove following statment

Let $X$ be a stochastic process defined on a probability space $(\omega ,\mathcal F,P)$ endowed with a filtration $(\mathcal F)_{t \ge0}$ and let $T$ , $T^\prime$ be $\mathcal F_{t}-$stopping times. ...
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11 views

R, probability, pbinom [closed]

According to literature, the average colony forming unit for my experiment is 23 CFU. I have 8 media plates. What chance is there that I can conclude from the 8 plates that the CFU is 20 or higher? ...
2
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1answer
33 views

Prove conditional expectation $E[X|X>x]$ is the unconditional expectation $E_{P^*}[X]$ under a probability measure $P^*$

Prove that the conditional expectation $\mathbb E[X|X>x]$ (here x is fixed, say x=10) is the unconditional expectation $\mathbb E_{\mathbb P^*}[X]$ under a probability measure $\mathbb P^*$. Derive ...
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2answers
99 views

Test predictions of football scores against a null model of “no predictive skill”

So, I am trying to prove that I can predict football scores better than randomly assigning win,draw or loss. I have predicted 140 scores, I have succeeded at 67. My null hypothesis is that ...
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3answers
115 views

Define the joint pmf of a particle moving randomly on a grid

A particle starts at (0,0) and moves in one-unit independant steps with equal probabilities of $\frac{1}{4}$ in each of four directions: north, south, east, and west. Let $S$ equal the east-west ...
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1answer
27 views

Find the pmf of a bivariate distribution when rolling a black and red four-sided die

Roll a pair of four-sided dice, one red and one black. Let $X$ equal the outcome on the red die and let $Y$ equal the sum of the two dice. Define the joint pmf on the space. So far I have $X = ...
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0answers
55 views

Conditional Probability of a variables given five independent variables

I have six independent variables A, B, C, D, E and F and I would like to compute the conditional probability of A given B, C, D, E and F. To illustrate the problem, is this answer correct? ...
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1answer
42 views

Modeling a process with decay and refilling

My question is about the approach that needs to be taken for modeling a particular process with . I have looked around for similar questions or answers but didn't find any. I got some links to Markov ...
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0answers
12 views

Two random variables each come from different distributions. How do I calculate P(X1>X2)? [duplicate]

I have X1~N(55,2) and X2~(48,4). Is there a simple math formula for calculating the probability that X1>X2? Thanks!
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0answers
17 views

Comparing values of random variables from sampled distributions

This is a novice question, which I struggling to answer. I want to find P(A>B) where A and B are random variables from two different distributions. Although two distributions that I have are not ...
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11 views

Calculate probability distribution $p\left(\left.X_{1:T}\right|Z_{1:T},y_{1:T}\right)$ in linear- non-Gaussian state space model

I have a linear, non-Gaussian state space model. Observation equation: $y_{t}=a+bX_{t}+cZ_{t}+\epsilon_{t}$ $\,\,\,\,$ $\epsilon_{t}\sim\mathcal{N}\left(0,\omega^{2}\right)$ Transition equations: ...
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0answers
10 views

Probability of reordering based on sample distributions

I am evaluating a computer system for which I obtained certain sample data, and I am trying to get some meaningful information from it, but I have only a basic knowledge of the statistics and ...
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1answer
16 views

Steady state Markov Chain

is it able to count the steady state of problem with recurrent subchain.. for example if there are A B C D things and they are all recurrent. do they have steady state?? and also.. how to count ...
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0answers
19 views

Probability that angle measure between two Gaussian vectors is less than threshold

Given $$r \triangleq \frac {\vec h^T \vec x } {||\vec h|| ||\vec x||}$$ $$\vec h \in \mathbb{R}^n,\vec x \in \mathbb{R}^n$$ $\vec h,\vec x$ are Gaussian i.i.d. vectors. I want to determine $Pr( r ...
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2answers
51 views

Given product has sold x times, what is the probability that a product will sell again?

I'm not sure how to look up and read about this problem, and I'm hoping you might be able to point me in the right direction. In essence, this question is about whether or not I should purchase ...
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0answers
13 views

Box of gold problem [duplicate]

The following question was posted on a social networking site. There was a disagreement as to the correct answer. Please provide an answer to help resolve the disagreement. There are three closed ...
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0answers
22 views

Sampling an N-dimensional copula via N independent uniforms

In order to draw a sample from an N-dimensional Gaussian copula, we draw N independent standard Gaussian random variables, form a vector, and multiply it by an appropriate matrix (Cholesky and such). ...
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If $E[X(t)X(s)]=t \land s $.Show that this process has independent increments

Let $X(t), t\ge0$ be a real-valued Gaussian process with mean zero and covariance function $E[X(t)X(s)]=t \land s $.Show that this process has independent increments.
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21 views

I want Find finite dimensional densities for an $\mathbb R^d-$ valued Gaussian process $X$with specified mean and covariance functions

Write the finite dimensional densities for an $\mathbb R^d-$ valued Gaussian process $X$with specified mean and covariance functions.
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1answer
56 views

Is $X_{(1)} + X_{(n)}$ a good estimator for $\theta$?

Problem 8.7 From Van der Vaart's Asymptotic Statistics: Given a sample of size $n$ from the uniform distribution on $[0,\theta]$, the maximum $X_{(n)}$ of the observations is biased downwards. ...
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2answers
79 views

How do i derive the joint probability distribution table of X and Y?

If there is a bag with 3 red balls, 2 blue balls and 1 white ball. Two balls are drawn without replacement. Let X be number of red balls drawn and Y be number of blue balls drawn.
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1answer
82 views

What is the probability of observing some function given a gaussian process?

I would like to compare a parametric function to a Gaussian Process. This may sound weird, but read on: Data description. I am looking at projections of a 3D object. However I expect a certain amount ...
2
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1answer
23 views

determining significance of term use

Thing one: feel free to RTFM me: I'm definitely looking for search-able terms or background reading. Our situation is this: we have a set of 140 reviewers and 20 elements. Each reviewer reviews each ...
3
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1answer
60 views

Guessing the length of a fish

I would like to solve the following excercise. Any help is appreciated. 90% of the fish in our pond are males, the rest are females. The length of the males are: $X+5$ inches, where $X\sim ...