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

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Linear discriminant analysis posterior not giving expected values in R

I have two normal distributions fg and bg with mean (mu) and standard deviations (sd) as follows: ...
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1answer
26 views

How to find the pdf of the difference beween random variables

Let $X_1,X_2,...,X_n$ be realizations of a random variable $X_0$. The realizations are obtained from the iterations of a discrete in time nonlinear dynamical map, $f(.)$ described as $X(n+1) = f^n(X(0)...
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What books are good for exam p for actuarial science

Hello I'm going to be a sophomore in college and planning on taking exam P for actuarial science. One of my weakest topic is probability. What "entry level" book would you recommend before I start ...
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1answer
29 views

PDF/CDF of max-min type random variable

For i.i.d. random variables, we may write the CDF of $t=\max(t_1,\cdots,t_N)$ as $$F_t(t)=F_{t_i}(x)^n$$ and the CDF of $x=\min(x_1,\cdots,x_N)$ as $$F_x(x)=1-(1-F_{x_i}(x))^n$$ When we have $X=\...
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1answer
39 views

Contradiction between the Law of Large Numbers and the Gambler's Fallacy? [duplicate]

If I flip a fair coin 10 times, and all of them land on heads, according to the Law of Large Numbers I am more likely to get tails on the next flip. However, this is clearly the Gambler's Fallacy. ...
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24 views

When is Latin Hypercube Sampling (LHS) a good idea?

In this paper: http://salserver.org.aalto.fi/vanhat_sivut/Opinnot/Mat-2.4108/pdf-files/emat08.pdf [1] equation 6 shows that if $\operatorname{ cov} \left(f\left(x_1\right),f\left(x_2\right)\right)$ is ...
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How do we know that the probability of rolling 1 and 2 is 1/18?

Since my first probability class I have been wondering about the following. Calculating probabilities is usually introduced via the ratio of the "favored events" to the total possible events. In the ...
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136 views

Probability of finding a new smallest value

I am doing some simulations and I need a good heuristic for when to stop the simulation. The simulation continuously outputs data with a cost in the range [0,1]. ...
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5 views

How do I know if LHS will reduce my sampling error?

In this paper: http://salserver.org.aalto.fi/vanhat_sivut/Opinnot/Mat-2.4108/pdf-files/emat08.pdf equation 6 shows that if $cov(f(x_1),f(x_2))$ is positive LHS does not reduce random sampling error. ...
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16 views

How can I apply discriminant analysis (multivariate) if my data is not normally distributed?

As LDA and QDA assume normality and homocedasticity, and my data is not that well behaved... is there any other kind of robust technique I could use? Could applying box cox transformations and then ...
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40 views

Calculating the probability of a successful marriage lasting N years

In reading the US HHS report on marriage trends, I was interested in calculating the probability that a marriage for a specific person with different qualities (male/female, education, race, age) ...
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9answers
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Probability of a single real-life future event: What does it mean when they say that “Hillary has a 75% chance of winning”?

As the election is a one time event, it is not an experiment that can be repeated. So exactly what does the statement "Hillary has a 75% chance of winning" technically mean? I am seeking a ...
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0answers
17 views

multivariate normal distribution. And marginals distributions [duplicate]

if $X_1$ and $X_2$ are random variables that marginally have a normal distribution, is it true that the joint $(X_1,X_2)$ has a distribution according to a multivariate normal density distribution? ...
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1answer
40 views

Conditional probability Bivariate Normal Distribution

$\newcommand{\Cov}{\operatorname{Cov}}$$\newcommand{\Var}{\operatorname{Var}}$$\newcommand{\E}{\mathbb{E}}$$\newcommand{\P}{\mathbb{P}}$We have that $X$ and $Y$ are random variables with a ...
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0answers
10 views

Help with conditional expectation of a convolution of multiple exponential random variables with different parameters

I'm working through this paper, with lots of help from all the great people on this site. Obviously my statistics/probability is a lacking to follow all the mathematical steps. Currently, I'm trying ...
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0answers
12 views

convolution of multiple exponential random variables with different parameters lambda

I'm trying to figure out the derivation presented on page 442 of this paper. Given a probability distribution $$f_n(t) \frac{\binom{n+1}{2}}{2N}\exp{\left(-\frac{t\binom{n+1}{2}}{2N}\right)}$$ ...
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1answer
46 views

What does penalizing a function mean, and how is it implemented?

I've alway seen this statement in academic papers, blog posts, documentation, etc. but I've never understood it. What does it mean to penalize a function, and what is a concrete example of it? Just to ...
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1answer
127 views

Is it always true that $P(X| Y \text{ OR } Z) \le P(X|Y)$?

Consider the following argument: If $(X| Y \ \text{OR} \ Z)$ is true, $(X| Y)$ must be true. For example, if $f(t)=10 $ when $ t=1 $ or $ \ t=0$ is true, then $f(t)=10 $ when $ t=1$ must be true ...
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1answer
33 views

Independence of random variables with known Gaussian conditional distributions

My question regards whether it's possible to know whether two Gaussian random variables are independent when we know only that their respective laws are governed by conditional distributions of ...
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18 views

proof of Markov chain Monte Carlo

This is the first step of proof of MCMC in my notes I have a question, how come $\pi(x)\pi(x_p\mid x)=\pi(x_p)\pi(x\mid x_p)$? Is it true for any markov chains which are ergodic and aperiodic? The ...
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31 views

exact value runtime for coin flip algorithm

So I have an algorithm like this: inc = 10 for num in Array: if num == 1: return inc else: inc += 1 inc += 1 return inc I want to ...
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0answers
16 views

Combining a classifier with average travel times

I'm working on the following problem: I'm trying to predict if a subway is moving or stationary based on the accelerometer profile that I collected with a phone. I used the acceleration data to train ...
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1answer
20 views

Regarding probabilites for naiveBayes algo

I have trained my data with naiveBayes algo in e1071 package. I have 6 classes in my data. I have predicted test data. the prediction returns only one class for each data point but I would like to ...
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23 views

Entropy of independent draws of balls from a bin

Problem Setting Consider a bin containing $B$ balls, each ball is red or blue with equal probability ($0.5$). Let $R$ denote the number of red balls. It is easy to see that $R \sim Binomial(B,0.5)$ ...
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Prbability Question [closed]

Suppose that the random variables X1, . . . , Xn form a random sample of size n from the uniform distribution on the interval [0, 1]. Let Y1 = min{X1, . . . , Xn }, and let Yn = max{X1, . . . , Xn }. ...
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9 views

Managing the growth of a distributed database

My database is composed of an increasing number of chunks, numbered from 0 onwards. At any given time, the size of database is $N$ chunks, having chunks numbered from 0 to $N - 1$. Every distributed ...
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2answers
26 views

How to calculate probability of success based on prior p-value

The FDA often requires a sponsor to conduct multiple clinical trials prior to approval. Given the following observations in a ph2 and ph3 trial, how would you go about predicting the probability of ...
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1answer
68 views

Help getting the variance of $Y$

We have $Z \sim N(0,1)$ and $Y=a+bZ+cZ^2$. What is the variance of $Y$? This is what I did: $$\mbox{Var} (Y)=0+b^2 \, \mbox{Var} (Z)+c^2 \, \mbox{Var} (Z^2) = b^2 + c^2 \, \mbox{Var} (Z^2)$$ To ...
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43 views

Calculating the probability to die in a card game using Markov chains

I saw this interesting question on reddit and couldn't figure it out. Situation There is a special card in the game seen below: Once this card gets played, there are 6 options that can happen. ...
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23 views

How to distribute overround over probabilities?

Is there any common pattern for distributing overround over the initial probabilities in bookmaking? Or it's up to bookmaker and they usually don't share it? UPD: Suppose we have some event with n ...
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1answer
29 views

On finding a confidence interval. (exercise)

I am having some problems with the second point of this exercise Let $(X_1, \dots, X_n)$ be a random sample extracted from a population $X$ that is distributed as a uniform $(0, \theta)$ and let $Y_n ...
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Is chi square test appropriate for testing frequencies of modifications?

I have a lot of sequence reads from next generation sequencing that I'm converting to a sequence of number of Stops, sorted by position on a specific gene. Such a sequence can look like: 0 0 0 0 1 0 ...
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10 views

How to solve unused argument? [closed]

I have a project using R package ‘actuar’. I wish to do loss distribution simulation for operational risk. In my screen design, I wish to find out the aggregate distribution for these severity and ...
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45 views

Is Robert Rutledge's calculation of the probability of similarities between Michelle Obama and Melania Trump's speeches reasonable?

Melania Trump has given a speech in support of her husband's campaign that many people believe has been plagiarised. An astrophysics professor, Robert Rutledge has calculated that there is a 1 in 87 ...
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2answers
61 views

Grandma and grandson share birthday but with a twist [closed]

Both me and my Grandson were born on October 10th. I in 1956 and he in 2008...he was born at 19:56 in the evening. What were the odds of that?
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5 views

Improve DBPedia results on Person

On running a query, such as: ...
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8 views

Objects and properties classification

I have a list of properties and objects: ...
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1answer
16 views

How to compute bounding coefficients for McDiarmid's inequality?

I am trying to understand the proof in Sec. A2 of Gretton et al.. To make the question self-contained, I summarize below the key ingredients. At the end of the post, I state my question. Given a ...
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23 views

Is my notation here reasonable? (basic probability)

Disclaimer: this is a homework problem, but I'm not asking for the answer I already have it. What I'm wondering is if a specific way of writing part of the problem is correct or not. I have other ways ...
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1answer
63 views

On some manipulations of $E[( X - tY)^2 ]$

I am following some notes and don't fully understand a step: call $0 \le f(t) = E[ (X- tY)^2] $ then by linearity of the expected value we get $$f(t) =E[Y^2]t^2 - 2 E[XY]t + E[X^2]$$ As noted this ...
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14 views

What is a good way to determine a major change has began in a set of numbers?

I'm visiting you guys from Stack Overflow because I need some non-programming related help with a project. So I am reading in a thermal image and trying to detect where the start of someone's head is. ...
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what's the equilibrium for this special birth-death process?

I have worked out questions from i to iii, no problems with that. But I don't know how to answer question iv, the note says that "The system reaches an equilibrium for all λ and μ except the trivial ...
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0answers
21 views

Conditional CDF and PDF equivalence

Imagine there are two random variables $X$ and $Y$, with CDFs given by $F(x,y)$, and corresponding marginals $F(x)$ and $F(y)$. There exists a PDF, given by $f(x,y)$, with marginals $f(x)$ and $f(y)$. ...
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42 views

Layman explanation of Cramér–Rao bound [closed]

I am trying to understand Cramér–Rao bound, but I have a problem understanding the formula in Wikipedia. Can somebody tell me the intuitive way of it?
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70 views

How to determine a prior, if there is no relevant prior empirical information?

I am using Bayesian probability. In my case, I have an empirical prior probability to use in calculating the posterior probability. But this isn’t the subjective way of doing it, I believe. If I didn’...
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66 views

R - What is the probability of a Value being *lower* than another value in a data frame

Here is a minimal dataset for this question: ...
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0answers
29 views

Calculating probabilities for 3, 4, 5 card Straight/Flush/Straight Flush With 5 Card Hands

(Originally posted on poker.stackexchange.com) I am playing around with creating a new card game, similar to poker, and I am really struggling with figuring out the math behind calculating the ...
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298 views

Wikipedia entry on likelihood seems ambiguous

I have a simple question regarding "conditional probability" and "Likelihood". (I have already surveyed this question here but to no avail.) It starts from the Wikipedia page on likelihood. They say ...
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54 views

R: Using Poisson statistics to predict terrorist attacks in France [closed]

I am a French data analyst and am pretty certain that a statistical description of the terrorist attacks would be possible, and even useful. As "rare" events, I would choose the Poisson probability ...
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34 views

Linear regression based classification

I'm trying to model a variable using bilinear regression as $y = ax + b$, Where $y$ is a scalar dependent variable, $x$ is the independent vector variable, a is a vector of two weights and b is the ...