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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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0 votes
1 answer
60 views

Solution of an implicit integral equation

The present question is pretty similar to this one. Here I want to find the solution of the following implicit integral equation: $$ P_H(u)=\int_{-\infty}^\infty dJ \int_{-\infty}^\infty du_1 \int_{-\...
-4 votes
2 answers
109 views

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. ...
0 votes
2 answers
172 views

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 ...
0 votes
0 answers
52 views

Unfair coin toss with conditional event [closed]

An unfair coin is flipped four times. The probability of a heads is 0.6 and the probability of a tails is 0.4. Every flip is independent of every other flip. Find the probability of getting exactly 2 ...
-1 votes
0 answers
36 views

Conditional Probability for A and B [closed]

My answer is graded as incorrect however I do not see any other way to do this. What am I missing? Given P(A)=0.7, P(B)=0.5, P(B|A)=.06 Find P(A union B) P(A union B) =P(A)+P(B)- P(A intersection B) P(...
0 votes
0 answers
33 views

The "StandardGaussian" bandwidth selection method in the SmoothKernelDistribution function

I have a list of points which follow the Gaussian distribution: ...
-4 votes
3 answers
165 views

Unable to check own distribution

Good afternoon I need to estimate different distributions from some data. Among these distributions, it is necessary to use the Kritsky-Menkel distribution. I set a formula for the distribution ...
1 vote
1 answer
163 views

Non-Gaussian Hidden Markov Process

I'm using EstimatedProcess to simulate a HiddenMarkovProcess with two states using data derived from different ARIMA processes <...
-3 votes
4 answers
260 views

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 ...
2 votes
0 answers
46 views

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: ...
3 votes
1 answer
206 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 ...
3 votes
1 answer
426 views

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. ...
0 votes
1 answer
85 views

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 ...
6 votes
6 answers
355 views

How to select elements from a list using another list

I have two lists: list1 and list2: ...
2 votes
3 answers
125 views

How to find the regression line equation of these two groups of data and draw the scatter diagram and regression line?

These two sets of data are as follows: ...
1 vote
3 answers
140 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-...
0 votes
0 answers
84 views

How to find a fit for the following data?

Consider the following function: ...
1 vote
0 answers
35 views

How can I compute probability of a simple predicate for 2-dim Normal distribution

The following code does not work: ...
0 votes
2 answers
563 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 <...
9 votes
3 answers
342 views

Obtaining formula of $E[X^T A X B X^T CX]$ for Gaussian $X$

Suppose $X$ is an $m\times n$ random matrix where rows are I.I.D. samples $x$ of $n$-dimensional Gaussian. The code at the end of the post verifies a candidate (incorrect) formula for the following ...
0 votes
0 answers
37 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 ...
1 vote
2 answers
129 views

The problem of finding the maximum coefficient term in the binomial expansion, find the value range of K

The problem is shown in the figure, and the result should be the range of K obtained at the end of the image ...
1 vote
2 answers
971 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
1 vote
1 answer
41 views

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 ...
0 votes
1 answer
39 views

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: $\mu = \sum_{i} x_i \cdot P(x_i)$,...
1 vote
1 answer
162 views

Can this previously solved three-dimensional constrained integration also be solved with certain added products in the integrand?

In Solved3DConstrainedIntegration the constrained three-dimensional (Hilbert-Schmidt-metric-based HSmetric) integration problem for the absolute separability probability of the two-qubit (quantum bit)...
6 votes
5 answers
1k views

How to calculate the number of prime numbers in a group of numbers?

If two different numbers are randomly selected from seven integers from 2 to 8, what is the probability of the two numbers being mutually prime? Take 2 different numbers randomly from 7 integers from ...
7 votes
3 answers
197 views

FindPeaks in a 2d list and half values

FindPeaks is a nice little help. But it only works on 1D lists and tends to return half integer values for positions of the peaks which are ultimately very useless ...
0 votes
1 answer
79 views

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 ...
3 votes
3 answers
175 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?
1 vote
0 answers
78 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 ...
0 votes
1 answer
52 views

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
4 votes
4 answers
84 views

Mean of List of Coordinates

Imagine I have the following list l = {{1, 2}, {1, 3}, {2, 4}, {2, 2}, {2, 3}} I want to take the mean only regarding the second element. That is, I want to find ...
0 votes
0 answers
51 views

How to quickly sample points according to the given distribution?

Consider the following points sampler: ...
0 votes
2 answers
82 views

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 '...
9 votes
5 answers
844 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 ...
1 vote
1 answer
77 views

How to compute a weighted mean as a measure of central tendency?

Imagine I have data points in triplicates, as follows $$ L=\begin{pmatrix} p_{11} & p_{12} & p_{13}\\ p_{21} & p_{22} & p_{23}\\ & \vdots &\\ p_{n1} & p_{n2} & p_{n3} \...
5 votes
1 answer
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 ...
1 vote
1 answer
157 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 ...
1 vote
1 answer
308 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 ...
9 votes
1 answer
449 views

Can LearnDistribution learn conditionality?

I would like to apply LearnDistribution to multivariate conditional distributions. Here's a simple artificial example: ...
2 votes
0 answers
60 views

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 ...
2 votes
4 answers
229 views

Does TTest taking into account the Welch's t-test?

TTest has an option VerifyTestAssumptions for "EqualVariance", does it automatically switch to Welch's t-test when variance of the two data sample differ a lot?
5 votes
1 answer
103 views

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 ...
0 votes
1 answer
66 views

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, ...
7 votes
4 answers
363 views

Getting formulas like $E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+10n^2+4n$

Suppose $A$ is an random $n\times n$ matrix with standard normal entries. A user was able to obtain the following formula by enumerating all diagrams by hand: $$E[\operatorname{Tr}(A^3 (A^T)^3]=n^4+...
1 vote
2 answers
152 views

The best way to guess the needed data using Mathematica?

I have a question, which is not entirely related to Mathematica, and would appreciate any help on this matter. I have the following dataset, which shows the growth of a bacterium in a specific medium: ...
2 votes
1 answer
69 views

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,...
6 votes
2 answers
233 views

How do you create the Commonest function

How does the Commonest function work? How can I implement that functionality without using that command?
1 vote
1 answer
146 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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