# 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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### How can we solve this probability problem through code?

Person A and Person B each have four cards, with each card marked by a number. Person A's cards are marked with the numbers 1, 3, 5, 7, and Person B's cards are marked with the numbers 2, 4, 6, 8. ...
• 4,697
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### Log Pearson Type III Distribution

Has anyone managed to implement the Log-Pearson type III distribution in Wolfram. To determine the parameters of the distribution over the data array using the FindDisributionParameters function? Here ...
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### The "StandardGaussian" bandwidth selection method in the SmoothKernelDistribution function

I have a list of points which follow the Gaussian distribution: ...
• 71
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### Expectation of area of random projection [closed]

I am thinking about a solution with Mathematica of a problem from 14th Kolmogorov competition (2015) on probability A planar polygon in three-dimensional space is projected onto a randomly chosen ...
• 27.4k
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### LaTeX symbols inside Expectation [duplicate]

I use LaTeX in my Mathematica code (using "^+4"), and was surprised that the first line in the code below evaluates correctly, but the second (essentially identical) line does not: ...
211 views

### How to use Mathematica to find the maximum expected value of multiple normal distributions?

Is it possible to calculate the maximum expected value of $n (n\geq 2)$ independent (identical distributed) random variables that follow a normal distribution? If possible, how to find it? If it ...
• 1,755
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### Plot fails to plot. What am I doing wrong?

The below code executes. If I uncomment the Plot, it runs for a while and outputs nothing, not even the Mean and Variance. ...
1 vote
141 views

### Integrating the derivative of a distribution via Expectation

Let's suppose to have a Multinormal distribution MultinormalDistribution[μ,Σ] . We can easily and very fast compute expectation values of the moments via the pre-...
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### How to find a fit for the following data?

Consider the following function: ...
• 5,895
1 vote
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### How can I compute probability of a simple predicate for 2-dim Normal distribution

The following code does not work: ...
45 views

### How to extract viewership data and what kind of distribution should describe youtube viewership for events in a video?

This is actually a 2-in-one question. I am a big chess fan, and I have been following the FIDE candidates tournament closely. I was watching an older interview where IM Levi Rozman interviews GM Ian ...
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1 vote
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### Issue with FullSimplify in StirlingS2 definition

I have previously asked a question about a problem simplifying an expression in Mathematica. The solution was to expand the definition of StirlingS2. This time, I ...
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### Problem calculating mean of probability distribution

I have a discrete probability distribution where $P(X=x)=(Factorial[n]/(n^x))*StirlingS2[x-1,n-1]$. So, when trying to calculate its mean with the following property: $\mu = \sum_{i} x_i \cdot P(x_i)$,...
• 145
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### Attempting Data Analysis with FlightData lnformation

I am trying to use data collected from the FlightData[] command to analyze departure delay data for a school project. I am getting as far as using a command to get the data, taking it into a named ...
1 vote
82 views

### Is there a difference in the definition of the pth percentile in Mathematica? [closed]

The pth percentile of a set of n data can be calculated by the following steps: Step 1: arrange the original data in ascending order. Step 2: calculate i=n*p%. Step 3: if i is not an integer and the ...
• 4,697
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### How to solve a problem about data when a certain percentile number is known?

Given that the 75th percentile of the data set is 6, how can we find the value of parameter a? data = {1, 1, a, 4, 5, 5, 6, 7} Why didn't the following method ...
• 4,697
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### Computation of critical value in F-distribution [closed]

Is there a way to manually compute the critical value of f-distribution from this table for df1=df2=417? It should be 1.21194 Thanks
190 views

### How to use Mathematica to find the mode of a set of data? [closed]

Mode[{2, 3, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10}] Why can't the mode command be used to find the mode of a set of data?
• 4,697
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### How to quickly sample points according to the given distribution?

Consider the following points sampler: ...
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### NExpectation with complex condition

When I run a computation for NExpectation with a condition of the following form -- T>R>P -- the computation runs fine. But when I add another inequality -- T>R>P>S -- it gives me an '...
212 views

### P-Values For LinearModelFit Changing Due To Ordering Of Features

The arbitrary ordering in a linear model of the independent variables should not impact the p-values for the coefficients of said model. However that is exactly what is happening here ...
860 views

### Create n random points on [0,1] with minimum distance

Given a positive integer n and a small positive real number s. How to create distribution for ...
• 4,325
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### Equivalent of MomentConvert for free moments/free cumulants? [closed]

I'm looking for Mathematica implementation of conversion between free moments and free cumulants. For instance, for traditional moments we have from ...
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### Alternative Representation for Energy Levels and Energy Level Density (II)

Following my previous question, I want a graph that must look like this (the lower image is taken from the Wikipedia page for the Microcanonocal Ensemble-->> Quantum Mechanical), The code for ...
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### Estimating the shape of the distribution of histogram

Here is the data: data = {37., 76, 81, 81, 28, 29, 18, 18, 27, 44, 18, 17, 70, 87, 45, 32, 88, 20, 18, 44, 17, 51, 24, 37, 24, 21, 18, 18, 17, 44, 25, 16, 45, 31, 74, 38, 16, 35, 17, 44, 34, 27, 87, ...
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1 vote
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### Joint Moments of Stochastic Process at Different Times

Suppose I have a random process defined in Mathematica, e.g. h = TelegraphProcess[a] I know you can use Mathematica to calculate different statistics like the mean,...
1 vote
182 views

### How to randomly sample small rotations?

I need a random rotation matrix that rotates random vectors by $\approx \arccos 0.9$ RandomVariate[CircularRealMatrixDistribution[n]] gives rotation matrices that ...
• 7,905
1 vote
152 views

### How to do BayesianMinimization in 2D?

Studying a new experimental BayesianMinimization command in 14.0 and following an example from the documentation ...
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### Expectation of a positive random variable gives negative results

Using Expectation to find $E[\operatorname{score}^2]$ evaluates to $-\frac{1}{6}$ below, why is this happening? ...
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### Why can't "TransformedDistribution" give a result but finding the probability first and then the derivative can?

PDF[TransformedDistribution[Sin[X], Distributed[X, ProbabilityDistribution[2*x/(Pi^2), {x, 0, Pi}]]], y] // Simplify produces ...
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### Calculating conditional expectation for uniform distribution over a trapezoid

I have a bivariate uniform distribution, defined over a trapezoid $\Omega$ with vertices $(2, 2), (1, -2), (-2, -2), (-2, 2)$: $$\vec{\xi} = (\xi_1, \xi_2) \sim \mathcal U (\Omega).$$ How can I ...
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### Computing statistics of sample average over $n$ IID variables

I need to plot $E[\log|1-a X|]=0$ as a function of $a$ where $X$ is sample average of $n$ IID draws from standard $\chi$^2. The following is a symbolic approach (borrowed from here) which works for \$n=...
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1 vote
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### Solving a System of Recursively Defined Equations in Mathematica

I am trying to solve a system of equations in Mathematica where the variables are recursively defined. The system represents a probability distribution, and I want to find the values of the variables ...