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

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18 views

Comparison of Bernstain and Chebyshev inequalities applied to Bernoulli distribution - simulation in R gives unexpected results

I'm trying to compare Bernstein and Chebyshev inequalities applied to Bernoulli distribution with parameter $p$. More specifically - how good are bounds they give for different sample sizes. I wrote ...
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8 views

Scikit Random forest pred_proba gives rounded off values

I am using random forest in scikit learn for classification and for getting the class probabilities , I used pred_proba function. But strangely it outputs probabilities rounded to first decimal place ...
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1answer
42 views

Optimization of Complicated Function with Two Random Variables

I am trying to find $x$ that will minimize the following expression which involves two sources of randomness. I am stuck and not even sure where to start. Any suggestions would be appreciated. Please ...
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0answers
32 views

Checking Markov Property [duplicate]

Let $\{X(n);n=0,1,2,\dots\}$ with state space $\{1,2,\dots,m\}$ be a stochastic process. Given transition probability matrices {P(n);n=0,1,...} (slowly varying) representing the probabilities of going ...
2
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1answer
189 views

Interpretation of a 95% confidence interval calculated via bootstrapping?

I've been thinking about what exactly a 95% confidence interval means when it is calculated via bootstrapping. The formal definition of a 95% confidence interval is something like this: "if the ...
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0answers
31 views

Probability of customer returning

I have all transaction history for a customer and would like to compute the probability that she/he will return. I think I can compute this is by computing the population mean of visits/30 days on the ...
0
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1answer
24 views

Joint inclusion probability for Horvitz–Thompson estimator

There is a Wikipedia page for the Horvitz–Thompson estimator. It is an estimator for the population total. Unfortunately the page has failed to state the standard error. From here, the standard ...
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0answers
10 views

Consistency of values of coefficients ($\alpha$) in Adaboost

Based on the given set of data, Adaboost learns weights($\alpha$) corresponding to the weak classifiers. Now suppose that there is a huge chunk of data broken down into smaller parts, e.g: a total of ...
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2answers
685 views

Likelihood of 10000:1 probability happening exactly once in 10,000 tries

I am interested in understanding the difference between "likelihood" of a random event with a particular probability actually occurring the exact probability it is said to be likely. i.e. if an event ...
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0answers
129 views

Joint and Marginal distributions in multichannel images

I want to know if the formalism for joint and marginal probability distributions applies to multichannel images. Consider the example below, written in Mathematica: Belos is the histogram showing ...
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0answers
30 views

Confusion about joint and conditional probability

A person has 16 headaches (H) in 30 days, means P(H) = 16/30 = 0.53 The person tracked his Stress Level and Lack of Sleep for those 30 days. It is assumed that High Stress (HS) and Lack of Sleep ...
0
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1answer
21 views

Order Statistics Conditional Distribution of Affiliated System

We have a system with $M (M\ge 2)$ random variables. The M variables are related as follows. For each i, 1 to M, $X_i = I_i+Z$, where $I_i$, Z are independent uniform random variables. What is the ...
4
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2answers
74 views

If each airline flight has a 2.6 in 1,000,000 and a person goes on 1000 flights, what are the odds for that person?

I would like to understand the way to calculate this particular problem. I understand that each flight still has a 2.6 in 1M chance of accident. But a person who takes more flights would seem to be ...
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0answers
25 views

What would be more flexible alternative to the Dirichlet distribution that is still “nice”?

Let's assume that I have some measurements about the total mass of certain compound. These measurements are very accurate so let's assume that the mass is just 1 (unit) in each case. Then I know that ...
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0answers
15 views

Calculate joint probability from dependent probabilities

I would like to calculate the joint probability $P(T,S)$ given a topsoil thickness probability $P(T)$ and a slope gradient probability $P(S)$. For the sake of disclosure, the slope gradient ...
2
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1answer
52 views

Estimating frequencies of a population

I have a sample of size 1121 from a population of size 2171 and I don't have access to any additional samples. The counts are ...
2
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3answers
149 views

Extrapolating the meaning of a probability

If I have 39% of students at a school that exhibit a specific, objective, measurable behavior, can I extrapolate this and say that any student at that school has a 39% chance of exhibiting that ...
2
votes
1answer
76 views

How to calculate joint probability based on result of two conditional probabilities?

I have P(Headache|Stress) = 0.88 where Stress is a "necessary" cause. Again, I have P(Headache|Coffee) = 0.35 where Coffee is also a "necessary" cause. Now I want to calculate joint effect of Stress ...
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2answers
96 views

Interpretation of confidence interval

Note: apologies in advance if this is a duplicate, I didn't find a similar q in my search Say we have a true parameter p. A confidence interval C(X) is a RV that contains p, say 95% of the time. Now ...
3
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2answers
172 views

Probability of agreeing to do some work depending on the payment

I am looking for several options of modeling the probability of people agreeing to do some work depending on the price/payment. The payment can only range between p1 and p2 (p1 < p2). I looked at ...
2
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0answers
27 views

Conditional probability with multiple dependent conditions

A set of items is said to be incorrect if at least one item in the set is incorrect. Initially, all items have equal probability of being correct/incorrect (P = 0.5). A series of infinite events ...
2
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0answers
13 views

Randomly Generating Combinations From Variable Weights

The Question I have a list A of n unique objects. Each object Ai has a variable percentage Pi. I want to create an algorithm that generates a new list B of k objects (k < n/2 and in most cases ...
5
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1answer
44 views

Runs of the same type within a deck of cards - distribution of runs of different length

My background is in Physics, not statistics, so forgive any suspect terminology or notation, but I hope the problem is clearly set out below. Secondly, my statistics is not good enough to recognise ...
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14 views

Lognormal and radial

Is lognormal distribution a class of radial distribution? P.S Gaussian, truncated Gaussian are all classes of radial distribution.
3
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1answer
26 views

Large Increase in Naive Bayes Accuracy results in decrease precision?

I am trying to classify (37 possible classes) a dataset that has 9 features and 900,000 occurrences. I have tried a couple different algorithms but the one that gave the lowest logarithmic loss was ...
2
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1answer
36 views

How does one do Stochastic Gradient Descent (SGD) on an objective function that has a regularizer?

I know that for Stochastic Gradient Descent, one picks a data point $(x_n, y_n)$ at random from the training set $S_N$ and then updates the parameter of the model in question. If the cost function ...
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3answers
60 views

How to calculate the time of finishing all tasks with probability of 90%

I have n tasks to do. I don't know how much time exactly it will take to finish given task so let's assume that each task on average k_n with standard deviation std_n to take (we can assume that the ...
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0answers
19 views

Calculating Bayesian Probability for Multiple “Tests”

I'm wanting to calculate the Bayesian probability of a Stock price going up or down based on multiple indicators. There is an abundance of clear literature on calculating the Bayesian probability for ...
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2answers
38 views

New to the field of stats, trying to apply it to my day job (cost estimating)

So to preface, I am very new to the world of Stats / quantitative analysis (I have recently gone back to uni and the paper I just completed is QA, specifically Regression, Estimation, Hyp. testing, ...
8
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1answer
111 views

Convexity of Function of PDF and CDF of Standard Normal Random Variable

Please provide proof that $Q\left(x\right)=x^{2}+x\frac{\phi\left(x\right)}{\Phi\left(x\right)}$ is convex $\forall x>0 $. Here, $\phi$ and $\mathbf{\Phi}$ are the standard normal PDF and CDF, ...
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63 views

Conditional PMF for $P_X(x) = \frac{2(x - a + 1) }{(b-a+1)(b-a+2)}$

The PMF of random variable $X$, is given by: $$P_X(x) = \begin{cases} \frac{2(x - a + 1) }{(b-a+1)(b-a+2)} & a \leq x \leq b \\ 0 &\mathrm{otherwise}. \end{cases}$$ Assume $a < 0$ and ...
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3answers
43 views

How to Randomly Generate SAT Scores in R with max and min?

I'm trying to figure out how to randomly generate SAT scores in R by subsection. It follows the general form rnorm(n,mean,SD), but I also need to take into account that the minimum value has to be 200 ...
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123 views

Conditional Expected Value of Product of Normal and Log Normal Distribution

Could someone please provide the answer and steps to solve this expression? \begin{eqnarray*} & & ...
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0answers
12 views

Bhattacharyya Distance for Age/Gender Groups?

I'm calculating distances for groups based on Age/Gender Compositions (to rank their similarity in demographic composition.) I'm working with the following: Men 18-34, Men 35-49, Men 50-64, Men 65+, ...
2
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1answer
52 views

Calculating probability for a continuous time markov chain

I can do question 1-3 no problem however I cant follow the steps to get the answer to part 4. Can anyone here explain the steps I need to go through in more detail?
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0answers
9 views

Which tool would be best analyzing human body movements and another persons reaction to it

Im wanting to look at specific movemnts of body parts over time and see if person A responds to person B in a certain way everytime/most of the time/some of the time person B does something specific.. ...
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2answers
246 views

Intuition for this observation//how restrictive is this assumption?

For many common continuous unimodal distribution function $F$ with density $F'$, I find that the derivative (wrt $x$) of $$(1)\quad \frac{F'(x)}{F''(x)}$$ i.e. $$\frac ...
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0answers
19 views

Making a table of probabilities

I apologize if this is the wrong board - I couldn't think of somewhere better to put it. I am making a table, going from higher certainty to lower certainty. It represents the probability that two ...
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1answer
28 views

how to calculate the following conditional probability

There are two events involved, say event A and event B. I want to know the probability of event B conditioned on the event A. The relation between the two events are as follows. We can not talk about ...
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0answers
10 views

How to compute the likelihood of a sample within a process containing gaussian and Non-gaussian noise

First, I'm sorry if the topic doesn't reflect the essence of my question very well, I don't have a very good statistical background. I've got a random variable, that is subject to two sources of ...
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0answers
20 views

Incorporating uncertainty in hypergeometric probability test

Wikipedia's page on determining the hypergeometric probability describes the variables in the following way: N is the population size, K is the number of success states in the population, n ...
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1answer
55 views

Measure the similarty between two sequences of letters

I'm trying to measure the similarity between two time-series sequences of letters with different lengths (e.g. s1=[A;A;A;C;B], s1=[Q;A;A;A;A;A] ). The order is very important. (e.g. s3=[A;A;A;C;C;C;C] ...
2
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1answer
14 views

weight a rating system to favour more severe cases

I have a rating system which can take 5 possible outcomes, which are coded to: ...
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0answers
27 views

Predictive model for Turnover - Correlation or Survival Analysis

Question 1 - I a working on developing a model to predict employee turnover. The variables that I have are age, tenure, job satisfaction, role clarity etc. Through research papers I have found the ...
2
votes
3answers
67 views

Conditioning on vs. fixing a random variable

I am confused by the following notation, seen used by a professor in a course I'm taking. $p(X|Y)$ denotes the conditioning of a distribution over a random variable $X$ by $Y$ and $p(X;y)$ denotes ...
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0answers
36 views

“Luckiness” measure for series

I have the following game: One player drops a coin N times. The probability of heads for each experiment is different and equal Pn. All probabilities are known(Actially there are only 10 different ...
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37 views

Chance of a virtual horse winning a virtual race

Every second, each horse has X chance of moving one step. H is a list of the chances of each horse moving: H = [X1, X2, X3...Xn] The race is won when any horse reaches it's 20th step. I need ...
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1answer
30 views

Time to completion

Say a person needs to go from A to B and also needs to complete a task. He may complete the task at either A or B. The task, say, takes 10 minutes. It takes 60 minutes to go from A to B after boarding ...
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19 views

Apples & Oranges?: Weighting Individual Rates to Calculate An Overall Hit Rate

Imagine that you have a training program. This program graduates 1,000 students. 350 of these student seek continuing education after graduation, and 650 seek immediate employment. Of those 350, 212 ...
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0answers
24 views

The infamous cross device identification and how to go about it

I am trying to work on a cross device user identification problem wherein I have mobile data,that is apps visited and mobile attributes; as well as browser data via cookies, that is websites visited ...