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

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3answers
43 views

Probabilistic Interpretation of Linear Regression

So this has been something I've been studying for some time. The first time I studied it I glossed over the details and parts that I really didn't understand. Now I'd like to tackle these points. My ...
1
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1answer
17 views

Conceptual problem for binomial distribution

I'm reading this book (Implementation: How Great Expectations in Washington Are Dashed in Oakland. 1973) and they discuss how hard it is to gain agreement of actors. They set up a conceptual ...
3
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1answer
48 views

Birthday Paradox: does it count if people are born in the same year?

Does the birthday problem change if we only take people from the same year (e.g. a classroom)? Intuitively I think it does, because you have more probabilities to have two people born in different ...
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0answers
22 views

predicting change in probabilities

I need some help in try to estimate some probabilities. I am trying to find the amount of home field advantage given when it comes to the pre game probability that the home team will when the game. ...
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0answers
22 views

Help solve a dice game problem that I came across [on hold]

If in the game of Yahtzee I roll 5 different numbers is it more likely to get a Yahtzee if I a. Pick up all the dice and roll again as I am not limited to any number b. Choose one of the numbers and ...
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0answers
45 views

Why does the normality of the coefficient's probability distribution follow from the normality of the errors in OLS?

So suppose after a simpple OLS regression we want to know what the chance(P-value) is that the Beta coefficient is 0 . First we assume that many random processes caused the errors ($\epsilon\!_i$), ...
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0answers
17 views

Trying to perform cluster analysis based on multi-variable data?

I’m struggling with how to find clusters/groups in a large set of multivariable data. Problem: Let’s say I have an ecommerce candy store. At my candy store I have various brands of candies(kitkat, ...
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0answers
25 views

Caclulating probabilty of drawing vector from multivariate normal distribution in R

given vector of mean $\mu$ and covariance matrix $\sigma$ as parameters of multivariate normal distribution, how can I calculate the probability of drawing $k$-dimensional vector from that ...
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0answers
41 views

Using Dirac Delta functions for estimating a probability distribution

I'm having some trouble understanding this slide. It's mentioned in the context of gaussian distributions. I sort of understand the Dirac delta "function". The main difficulty I'm having is with ...
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0answers
20 views

Project Success Probability [on hold]

If there are two years of projects, the first year project has probability 0.7 of being high, and there is a .30 probability that both years will have success, but a 0.10 probability that both ...
1
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0answers
38 views

Imposing a model on a pdf

(This question is an attempt to zoom in on the key issue in this question using as little information as possible.) Lets say I want to derive the likelihood function of $\beta$ given $x$ and $y$ for ...
1
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0answers
37 views

Derivation of likelihood function for latent variable model made explicit

I am trying to make the steps deriving the likelihood function for the following latent variable model as explicit as possible: $$Y^0=X\beta + u$$ where $$u \sim NID(0,\sigma^2).$$ The observed data ...
6
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2answers
139 views

A continuous function of a sequence of random vectors converges in probability to the function of the limit

Proposition: If $\{ X_n \}$ is a sequence of k-dimensional random vectors s.t. $X_n \overset{p}{\to} X$ and if $g: R^k \rightarrow R^m$ is a continuous mapping, then $g(X_n) \overset{p}{\to} g(X)$. ...
1
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0answers
28 views

Does the degree to which events are independent increase as the number of events increase?

I'm considering a problem of independence of events. Specifically, I am considering whether events are more independent the greater the number of events. Two examples might help. Example 1: There ...
0
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0answers
6 views

how to quantify the dependence between two sparse signals?

Hi and thank you for your help. I am happy to provide more context/details. In my research, I have a system that has many sensors X_1..X_N and using this ...
2
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0answers
21 views

Sum and product rules for continuous variables in probability

I have seen that a formal justification for the sum and product rules applied to continuous variables requires measure theory. Does anyone know where I can find this formal justification? The rules ...
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0answers
28 views

find the probability [closed]

According to FBI date, 12.4% of burglaries are cleared with arrests. A new detective is assigned to 5 different burglaries. What is the probability that at least one of them is cleared with an ...
0
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1answer
35 views

Proving the sum rule of probability limits

I'm trying to show that if $X_n$ converges in probability to 0 and $Y_n$ converges in probability to 0, then $X_n+Y_n$ converges in probability to $0$, ie the sum rule for probability limits. What ...
3
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0answers
72 views

How to sample from a distribution while the sample point simultaneously needs to satisfy an inequality constraint?

I have a Dirichlet distribution $P(x)$ , where $x$ is a point on a simplex. It is very easy to sample from this Dirichlet distribution. But I have a set of non-linear, non-convex constraints ...
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0answers
13 views

Marble bag odds

Given two people each with bags containing 88 white marbles and 2 red with a random mix, if both people draw 1 random marble at a time from their own bags, what are the odds that both draw the two red ...
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0answers
6 views

Reference for rigorous derivation of bigram model

The unigram model for bodies of text makes the assumption that in a given corpus the value of the $n$th word is independent of the $n-1$th word. Then, for a fixed dictionary $D$ and a corpus of text ...
1
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0answers
16 views

Different Methods for clustering skills in text

Consider a talent pool in which each member has some set of skills. Some of these talent are submitted to orders as potential candidates of which one is selected. It is reasonable to assume that the ...
3
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1answer
82 views

How many doors does a salesman have to knock before reaching x sales?

Imagine a salesman assigned to a neighborhood, each home has a unique and independent conversion rate associated with it that we might model like ...
2
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2answers
58 views

Proof of Algebraic Formula for the Sum of Two-Dice Toss as a Convolution

To figure out exactly the expected frequency of a given sum in a dice toss (given a certain number of dice and sides/dice), the following formula is posted here by @Glen_b (adapted to dice of six ...
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0answers
21 views

markov chain question [closed]

There are two points which are A and B. The distance between A and B is 50meter. One person goes to A with probability 1/6, he goes to B with probability 3/6. And he goes nowhere with probability 2/6. ...
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1answer
35 views

markov chain - probability question

Transition matrix has been written like that; $$\mathcal P = \begin{bmatrix} 1/3 & 0 & 2/3 \\ 1/3 & 1/3 & 1/3 \\ 0 & 0 & 1 \end{bmatrix}$$ the initial vector is that ...
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0answers
22 views

Chances of a reducing probability

Ok guys, please help if you can on this, it's foxed me! 9 people sat in a circle. They wrote their name on a piece of paper, folded it over and placed it in a hat. The hat was shuffled to mix up ...
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0answers
22 views

What does raising frequencies to a power do when calculating probabilities? [closed]

For example I read some code iterating through an array of frequencies: ...
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0answers
24 views

Using Boole's Inequality to Prove Observation

I'm walking through the book "Probability" by Jim Pitman book solo and cannot wrap my head around this problem; Use Boole's Inequality and the fact that, to prove. How do you approach this ...
7
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1answer
122 views

Mechanics behind deviation from random distribution

The system we are working on is biological, more specifically the distribution of programmed DNA damage events across a chromosome. This can be thought of as 1D array (the chromosome) across which ...
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0answers
15 views

Aggregated probability using irregularly-spaced time series data

I have dataset describing a group of animals' size and growth over 2 years. These particular animals grow in non-continuous growth steps and I wish to model the frequency of these growth steps during ...
6
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1answer
127 views

How to calculate the relative risk based on two independent confidence intervals

Medicine A cures 30% of patients (95% CI: 17 to 45). Medicine B cures 15% of patients (95% CI: 10 to 20). So I can divide 30% by 15% and say that medicine A is twice as likely to cure the patients ...
4
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1answer
71 views

Semicolon in probability expression

I run in to this formula when reading a tutorial: $$ \begin{align} P(\pi|\mathbf L;\gamma_{\pi1}, \gamma_{\pi0}) & =P(\mathbf L|\pi)P(\pi|\gamma_{\pi1},\gamma_{\pi0})\tag{28} \\ &\propto ...
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0answers
37 views

Why is Bayes theorem more popular than the normal definition of P(A|B)? [duplicate]

As everyone knows, the conditional probability of A given B is $P(A|B) = \frac{P(A\cap B)}{P(B)}$, and Bayes' theorem is derived from that equation to $P(A|B) = \frac{P(B|A)P(A)}{P(B)}$. I'm pretty ...
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0answers
15 views

How to show that $\pi^{X(n)}_{o}$ for $n \geq 0$ and $X(n)$ a branching process, is a martingale?

If I let $X(n)$ be defined as the size of a branching process at the $n$th generation, and $\pi_{o}$ as the probability that the process will eventually go extinct, I'd like to show that ...
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2answers
52 views

Odds vs probability in logistic regression

I am going through Trevor Hastie's Classification Techniques. Its says Odds are traditionally used instead of probabilities in horse-racing. I still don't understand how they relate more ...
2
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1answer
58 views

Prove that limsup of a sum of iid random variables(with 0 expectation) is infinity

Let $Y_1, Y_2, Y_3,\ldots,Y_n,\ldots$ be iid and bounded random variables with $E[Y_1]=0$. Define $X_n = Y_1+Y_2+ \cdots + Y_n$. If $\Pr(Y_1 \neq 0) \gt 0$, then $ \limsup X_n = \infty$ with ...
3
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1answer
49 views

Variance stabilisation

$Y$ has mean $\mu$ and variance function $V(\mu)$. If $V(\mu) = \alpha.\mu^v$ then $h(y) = y^{(2-v)/2}$ is variance stabilising which means that $Var(h(Y))$ is approximately constant. I tried to ...
17
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2answers
666 views

Does this discrete distribution have a name?

Does this discrete distribution have a name? For $i \in 1...N$ $f(i) = \frac{1}{N} \sum_{j = i}^N \frac{1}{j}$ I came across this distribution from the following: I have a list of $N$ items ranked ...
2
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1answer
34 views

Clarify probability solution re. birthdays

I have a problem regarding birthdays that involve the possible birthdays a group of 5 people can have within the 7 days of the week. My solution to this was 5^7 total possibilities, but I'm not sure ...
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0answers
24 views

Probability that a large corpus of text is generated with the same parameters as a subset

Let's say I have a process which generates different words at a set (unknown) frequency per word. I sample this process X times, generating the word "yo" Y times. I then look at a subset of my ...
1
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0answers
28 views

What does the notation $\chi_{(V\ge1)}$ mean in probability / statistics? [duplicate]

I reading Benjamini and Hochberg's paper on controlling the FDR, and I came across this notation "$\chi_{(V\ge1)}$" in section 2.1 paragraph (b), and I'm guessing from context that: $$ \chi_{(V\ge1)} ...
1
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0answers
79 views

Error in linear regression

Given two series $(x_1,...x_n)$ and $(y_1,...y_n)$, and assume that we know $x_{n+1}$. Given the fact that the pearson correlation won't change in the next observation of $y_{n+1}$, can we bound the ...
0
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3answers
49 views

A hypothesis test question

Let $X_i$ (for all integer $i$)be Bernoulli random variables (which takes either value -1 or 1, with equal probability). Define a random variable $Y$ to be $Y=\sum_{i=1}^d{X_i}$, where $d$ is a hidden ...
0
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1answer
23 views

How to compare 2 ARIMA model predictions using mean squared prediction error

How can I compare the predictions of 2 arima models using mean square prediction error in R, given that I know what the observed values are. Help greatly appreciated.
2
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2answers
95 views

Poker and the Birthday Problem

The number of possible poker hands drawn from a standard 5-card deck is ${52 \choose 5}$. This is sampling without replacement where order does not matter, e.g., ...
0
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0answers
13 views

Conditional probability with joint distribution gaussian [duplicate]

Given that $(x_1, x_2)$ are jointly normally distributed with $\mu = 􏰃\begin{bmatrix} \mu_1 \\ \mu_2 \end{bmatrix}$ 􏰄and $\Sigma = \begin{bmatrix} \sigma_1^2 & \sigma_{12} \\ \sigma_{21} & ...
0
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0answers
35 views

Dealing with a Summation within a probability

If I know the $P(Y_i = 1) = X$ then how can I determine the $P(\sum\limits_{i=1}^m Y_i = k)$?
4
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2answers
315 views

How can the “anti-correlation” between these two curves be shown?

I'm looking at data defined on a given feature with respect to two measures. Whilst both measures are defined on the same domain, both measures are defined on different ranges, so, with a view to ...
0
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0answers
29 views

Relationship between expectation and probability with continuous variables

I've tried to word this question to the best of my ability but I may have got some of the terminology wrong. Example: I have a machine producing various lengths of knotted string. If I have a string ...