Questions tagged [probability-or-statistics]

Questions about systematic data collection and organization, or the application of probability theory to model the inherent patterns and properties of sampled data, underlying data distribution(s) or random processes.

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0answers
35 views

Performance inconsistency: What's going on here?

Consider: ...
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2answers
47 views

How to make calculations involving symbolic summation?

I want to minimize a function involving the sum of $n$ fixed (but indetermined) $x$ values, for example: Minimize[Sum[(x[i] - a)^2, {i, 1, n}], a] Expected answer: ...
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1answer
21 views

multivariate Gaussian distribution with identity covariance

I want to draw Geometry (or contours) for multivariate Gaussian distribution with identity covariance matrix (or draw decision boundary). How this is possible via Wolfram's online at Here? Please ...
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0answers
32 views

Failure in MultinormalDistribution

My RandomVariate fails to evaluate when sampling from a multinormal distribution, any idea what's happening here? This is Mathematica 12.1 on Mac: ...
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3answers
81 views

What is the probability of the digit $k$ in the number $x^n$

Well, the title of the question says it all: how to write a code that finds the probability of the digit $k$ in the number $x^n$? For example, when $x=2$, $n=100$, and $k=7$ we are trying to find how ...
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0answers
35 views

Strange result for calculating $\Pr \left[ {X > \frac{2}{Y},X > \frac{4}{Y}} \right]$ with $X,Y$ follow exponential distribution? [closed]

First, when I calculate $\Pr \left[ {X > \frac{2}{Y},X > \frac{4}{Y}} \right] = \Pr \left[ {X > \frac{2}{Y}} \right]\Pr \left[ {X > \frac{4}{Y}} \right]$ with $X,Y$ follow the exponential ...
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1answer
88 views

Fisher information for a Gaussian

I would like to calculate the Fisher information for $f(x|\alpha)=\frac{1}{(2\pi \delta^2(\alpha))^{1/2}} Exp\{-\frac{(x-\mu(\alpha))^2}{2\delta^2(\alpha)}\}$ using ${\rm FisherInformation}[\{\mu, \...
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1answer
46 views

Fisher distribution expressed with Chi ²

I am learning about the ANOVA test. This involves the Fisher-distribution. I know there is the ANOVA function and the ...
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0answers
52 views

Histogram of the roll of a die during “n” trials [closed]

How can I get something like this example so that on the y-axis appears the number of tests and on the x-axis a histogram with the numbers from 1 to 6. The idea is that the bars accumulate the number ...
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0answers
28 views

Speed up exact distribution of the sum of the top $k$ statistics on a bounded discrete uniform distribution?

I came across a nice answer by Sasha (I believe a Wolfram engineer) on mathematics stack exchange regarding the distribution of the sum of the top $k$ order statistics. (This was an answer to an RPG ...
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4answers
1k views

Mean age of people [closed]

I have the following datas: I want to find mean age by using following formula, Any way to do this in general in Mathematica easily.
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0answers
39 views

Computing the Mean of Around Values

I understand the computation of the uncertainty of independent Around values to be based on the following first order approximation $$ \delta f(x,y)=\sqrt{\left(\frac{\text{$\delta $f}}{\partial x}...
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1answer
61 views

i need to simulate a roulette table where a perosn bets $10 on red 1 time, 5 times,20 times, 100 times and 10,000 times

I need to simulate a roulette table where a perosn bets $10 on red 1 time, 5 times,20 times, 100 times and 10,000 times, i then need to find out how much the person wins or loses once they play 10,000 ...
2
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1answer
53 views

Intepreting the results of DistributionFitTest, and other alternatives in Mathematica 12.1

I have been playing with DistributionFitTest as a means of testing how normal some data sets I have. I've been working with some simulated data sets so I can try ...
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0answers
45 views

Mann Whitney Test

I am trying to check data in Mathematica with the Mann Whitney Test. The author states: Mann–Whitney's U-test; U = 609, z = 2.07, p < 0.05. How would I put this ...
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1answer
126 views

How to plot this pdf

Let $x\sim N(\mu,\sigma^2)$ and $y=\max\{e^{x-1}-\kappa,0\}$. How to get and plot the pdf of y? In particular, there will be a probability mass at $y=0$, which is a nondifferentiable point. I tried <...
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1answer
53 views

Generating a set of random variates from Poisson distribution

Say I am not allowed to use built-in PoissonDistribution, which means I should generate 100 random numbers first, and then with these 100 random numbers to generate 100 random variates from Poisson ...
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3answers
117 views

How to simulate the roll of 3 or more dice and ask for a sum of 3 or more?

How to simulate the throwing of 3 or more dice and ask for the sum of 3 or more and indicate the number of calves, or more that are produced. For example if you throw 3 dice, how many cases will add ...
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2answers
167 views

Confirm and possibly simplify a 2009 result for a 2D constrained integration

This is a direct descendant of two other recent questions, 3D and Equivalence, both of which have been answered in skillful, interesting manners. (See also the comment [actually answer] of JimB to ...
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0answers
35 views

Piecewise function inside ProbabilityDistribution causing errors

I'm using a complicated Piecewise function to create a probability distribution and draw random points from it. ...
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1answer
48 views

How to emulate statistical command choice tab of this widget?-how to do what i ask?

I designed this little program, but I want you to be able to choose what I want to look for by choosing it as you do with the widget tab, please help me. widget Widget of internet my program ...
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1answer
44 views

Probability distribution with random paremeters

Is it possible to set something like this? A probability distribution with random parameters ...
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0answers
28 views

Unable to evaluate expectation of sum, but able to evaluate expectation of each summand

I would like to evaluate the expectation of the expression x + x Log[x] where x follows a generalised gamma distribution ...
2
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1answer
81 views

Turning a matrix matrix into a probability table

I want to build a probability table that is able to answer questions such as "if i roll 5, 4 sided dice what is the probability i get at least a 16?" My current code is: ...
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1answer
110 views

Evaluate 3D- and 5D-constrained integrals for absolute separability probabilities

In a recent posting, TwoQubits user JimB, employing a change-of-transformations put forth by N. Tessore, was able to confirm a formula for the "two-qubit absolute separability Hilbert-Schmidt ...
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0answers
31 views

Adding a module to teach Mathematica the Laplace transform of particular Mittag-Leffler functions

Mathematica 11.3 is not aware of a useful Laplace transform LaplaceTransform[t^(-a) MittagLefflerE[a, a, t^a], t, s] which for ...
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0answers
32 views

Plot the confidence interval bands from standard error and mean

My data has 20 horizons of mean and standard error. The very first step I'd like to manually calculate the 95% confidence interval from standard error and mean. After this, is to plot the timevarying ...
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2answers
73 views

Ideas to speed up an order statistic calculation?

A toy example: {n, top} = {25, 100}; mxs = RandomReal[{0, top}, n]; dist = UniformDistribution[Thread[{0, mxs}]]; result = Mean[OrderDistribution[dist, n]] With ...
3
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2answers
184 views

Simplifying the code to calculate probability of tossing 4 unfair dice

Four identical unfair dice are tossed once. Find the probability of events in which the sum of numbers (facing up) is 18. Given the probability of face 6 is $1/2$ and that of each other face is $1/10$....
2
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1answer
62 views

Concatenation of Distributions

I would like to calculate mean, variance, ... of a concatenation of distributions (is this the correct technical term?). For an easy example I am trying to calculate the mean of a PoissonDistribution ...
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0answers
27 views
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0answers
40 views

Total Variation Distance(between Gaussians)

I am interested in a tool that calculates the total variation distance between two multivariate Normal distributions. Any help will be much appreciated as I am a complete beginner.(So far, I have ...
4
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2answers
87 views

Commutation, symmetrizer and duplication matrices

The following 3 matrices are useful when viewing matrices as vectors, known as commutation $K_n$, symmetrizer $N_n$ and duplication $G_n$. They are usually defined by their matrix relations below. $$ \...
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2answers
293 views

Evaluate a certain three-dimensional constrained integral

The result of the three-dimensional integration ...
1
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1answer
90 views

Speeding up Gaussian expectations

I found that Mathematica's Expectation operator is slow for Gaussian random variables, I'd like to scale to 100 dimensions, but it currently takes 10 seconds for 10 dimensions, looking forward to tips ...
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0answers
39 views

Modeling geometric Brownian motion with an Ito process [closed]

I am trying to model geometric Brownian motion using ItoProcess. I am not sure why I am getting negative values in the output. I am not using ...
2
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1answer
97 views

Making animation based on COVID-19 data [closed]

There is an animation of the growth and spread of COVID-19 cases worldwide at http://www.healthmap.org/covid-19 My question is how do I make the same animation using Mathematica, also analyze the ...
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1answer
131 views

Probability poker game task

I have this task: And I've got this far in my mathematica program, however I can't figure out why my probability turns out 0? ...
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1answer
60 views

Expressions for moments of sample cumulants?

I sample $n$ points from standard normal and need the mean and variance of 3rd and 4th sample cumulants. @JimB suggested that variance of 4th sample cumulant is given by the expression below. This ...
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1answer
63 views

Help Calculating My “Deviation”

I created a "distribution deviation" where for $\left\{a_1,...,a_k\right\}$ we take all take the mean of all combinations of $\frac{\min\left\{a_{i},a_{j}\right\}}{\max\left\{a_{i},a_j\right\...
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1answer
51 views

Can the WishartMatrixDistribution command be used for generating random density matrices?

I am interested in generating random members of two classes of $n \times n$ positive-definite matrices $A$ and $B$--the former symmetric in nature, the latter, Hermitian. The standard (Ginibre-matrix-...
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0answers
75 views

Calculate a nested integral

I wish to plot the following probability on Mathematica: $$ \pi=n\cdot\int_{-\infty}^{+\infty}\int_{-\infty}^{+\infty}\left[\int_{-\infty}^{z_{1}}G\left(z-z_{2}\right)\cdot f\left(z_{2}\right)dz_{2}\...
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1answer
152 views

Can this probability function speed be improved?

I have a process that as part of it requires a certain probability query, specifically, given a multinomial distribution with f equiprobable categories and r trials, some specific category has a given ...
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2answers
74 views

How to define a function of probability addition formula

In probability theory, the addition formula of any event is as follows: $$P(A \cup B)=P(A)+P(B)-P(A B)$$ $$\begin{aligned} P\left(A_{1} \cup A_{2} \cup \cdots \cup A_{n}\right)=& \sum_{i=1}^{n} P\...
4
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2answers
62 views

EstimatdDistribution returns evaluated expression, not function name/

Ok, this takes a little bit o preparation. I'd like to estimate a distribution for some data. I have a distribution function that is not part of the canonical Mathematica set so I define it via ...
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0answers
19 views

Defining the support of a random variable in Mathematica [duplicate]

I wish to create a Mathematica module that would take as input a Mathematica-defined probability distribution D and will perform an integration over the support of its density f, $supp(f)$ (where $f:X\...
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0answers
29 views

Problem with FormulaLookup and FormulaData

I'm not getting an answer when I type either: FormulaLookup["BinomialDistribution"] or ...
1
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1answer
45 views

How to use the function `Covariance` to calculate covariance correctly?

Note: The following questions are from the 23th question of the 2005 Chinese Graduate Mathematical Entrance Examination (first set): Suppose $X_{1}, X_{2}, \cdots, X_{n}(n>2)$ is a simple random ...
2
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1answer
57 views

How meaningful, or useful, are parameter errors produced when perfroming an unweighted LinearModelFit or NonlinearModelFit?

This may be a question which teeters on the brink of belonging more to the realm of statistics and Cross-Validated SE, but I'm also specifically interested in Mathematica fitting routines. Usually, if ...

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