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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37 views

outcomes and payoff in probability games [closed]

I am reading probability from AI point of view from book Artificial Intellegence A Modern approach by Russel and Norving. Below is text snippet from chapter 13. One argument for the axioms of ...
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1answer
69 views

Evaluation points following a bivariate Gaussian distribution [closed]

I have a function of two variables, say $f(a, b)$, which I want to evaluate (and later average) in the neighborhood of $a=0$ and $b=0$, with density of points around $(a,\,b)$ following a Gaussian ...
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1answer
40 views

How to plot Log(P(x)) in a histogram?

I have been using SmoothHistogram to plot the probability density function $P(x)$ of some experimental data. On the y-axis, I would like to have $\log(P(x))$ ...
2
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1answer
95 views

Speeding up code doing random sampling

I have a particular probability distribution (that is a function of a parameter $\phi$), that I would like to sample from and then do a listplot for that function. Here is the code that I came up with:...
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0answers
43 views

Taylor expansion of expected value of a function with multiple random variables

The expected value of a function of multiple random variables can be approximated by a Taylor expansion. How this can be done in MMA is described in other posts (Link1, Link2). Let's assume we have a ...
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1answer
86 views

Problem with parameters from fitting

I am trying to fit the following data (called TflogqIND): ...
1
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1answer
64 views

Specifying statistical models / Equations between Random Variables [closed]

I'm new to Mathematica and confused about how random variables work. Say I have a standard normal random variable $X\sim \mathcal N(0,1)$ and set $Y := 2X$. Then $\operatorname{Cov}(X,Y) = 2$. Now if ...
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0answers
26 views

Computation of 1- and 2-sided p-values for Fisher's Exact test for 2x2 table based on Monte Carlo

I am looking for code to compute the 1- and 2-sided p-value for Fisher's Exact test for 2x2 tables based on Monte Carlo (bootstrap simulations). For larger 2x2 crosstabulation tables, the exact p-...
2
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0answers
52 views

Matrix regularization, how to pick $\lambda$

Since v12 FindFit[] now supports regularisation, such as Tikhonov regularization. Do there exist statistics to help guide the choice of the hyper-parameter $\...
4
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3answers
332 views

Calculate variance for a lottery?

I'm trying to calculate the variance for a lottery using the mathematica function "variance". In the following a simplified example with just a few values, and how I tried to solve it: ...
3
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1answer
94 views

Taking mean of a numerical function $f(t',x,y)$ [closed]

$f(t,x,y)$ is a solution from NDSolve, in a domain $\mathcal{D}$. If $f(t,x,y)$ was an analytical func I would $$\overline{f(t)}=\frac{ \int _{\mathcal{D}} f(t,x,y) dx dy}{\mathcal{D}}$$ Since $f(t,x,...
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2answers
106 views

Expectation with conditional random variable [closed]

Given an Exponentially Distributed Random Variable $X\sim \exp(1)$, I need to find $\mathbb{E}[P_v]$ in Mathematica, where $P_v$ is given as: ...
4
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3answers
160 views

Empirical mean excess plot of (μ, e(μ))

Say I generated n random variates from the standard cauchy distribution. I want to construct the empirical mean excess plot of (μ, e(μ)) , where e(μ)={Σ(xi-μ) *I {xi>=μ}}/Nμ . Nμ is the number of ...
0
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1answer
126 views

How to solve following equation with multiple random variables

How can I program the following problem into Mathematica? $X,Y$ are i.i.d. Exponentially distributed random variables. Such that $X\sim\exp(1), \ Y\sim\exp(1)$. All other variables are positive real-...
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2answers
63 views

Find intercept line and intercept point from data sets

If I have two set of data such as: ...
3
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1answer
139 views

Problem with fitting a given data with an equation

I want to fit a given data using the approach developed by @Bob Hanlon here: Fit and find fitting parameters of data given an equation I have tried this approach for several different data sets but I ...
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0answers
37 views

Moment generating function of Maxima $E[\exp(t \max(X,Y))]$

Let $X,Y$ be two standard normal random variables with correlation coefficient $r\in[-1,1]$. I'm trying to compute the moment generating function of the maxima using Mathematica: ...
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0answers
27 views

does Mma provide exact critical values of Mann Whitney U (small samples)

Does Mma provide exact critical values for the Mann Whitney U test, along the lines of haskell? Or just as good, for given two small samples, can I easily ask ...
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0answers
43 views

Problem with a BarChart

I have problems with a graph, First: I am using data from a list, before I used RamdomReal, but I can't get it to work. Second: the statistical data doesn't appear in the graph, I do not know why. ...
0
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1answer
91 views

Resources to learn probability with mathematica?

Can someone recommend me any resources to learn Probability with Mathematica. Hopefully a book that has mathematica exercises and code examples.
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2answers
155 views

Incorrect results in probability calculation [closed]

By my calculations ...
3
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0answers
61 views

How to reproduce SmoothKernelDistribution[] for the bivariate case

I am trying to reproduce the results of SmoothKernelDistribution[] for the bivariate case. ...
1
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2answers
99 views

Translating MATLAB code into WL code [closed]

I want to solve the following problem by simulation. There is a bus with 100 labelled seats (labelled from 1 to 100). There are 100 persons standing in a queue. Persons are also labelled from 1 to ...
6
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1answer
95 views

How to find individual probabilities of all numbers from a list? [closed]

I have the following list of random numbers: ...
3
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1answer
70 views

Probability Generating Function(s)?

I'm very new to Mathematica and I have started to use it since I have been tackling some Physics related problems(I'm an engineer by training). Specifically, I'm dealing with Master Equations and one ...
5
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3answers
247 views

Plotting a normal curve over a histogram

I am teaching a basic introduction to normal curves, and the textbook introduces the topic with the idea of rolling five dice and recording the sum. Do this many times and create a histogram of the ...
3
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2answers
109 views

Estimation of the expected Euclidean distance between two random points on a unit $n$-hemisphere

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance (in a $(n+1)$-dimensional space) between two points selected uniformly at random on a unit $n$-...
1
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1answer
72 views

How to find the inverse of CDF of geometric function? [closed]

The cdf of geometric distribution is given by $ F(x)=1-(1-p)^x$. I want to calculate the inverse of it, for example, $F^{-1}(U)$ I am doing the following ...
2
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3answers
134 views

Estimate the expected distance between two random points on the unit $n$-sphere [duplicate]

What is the best approach to estimate, with Wolfram Mathematica, the expected Euclidean distance in a $(n+1)$-dimensional space between two points selected uniformly at random on the unit $n$-sphere? ...
1
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2answers
71 views

TransformedDistribution of normal and skew-normal distributions

I have the following distributions: distC =NormalDistribution[251.563, 0.317394] distS =SkewNormalDistribution[252.973, 0.503173, 5.59741] I want to analyse what ...
1
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1answer
48 views

Implementing Random process for exponential correlation function

I'm trying to simulate a random process for a variable $-1<X(t)<1$ with average 0, i.e., $\left\langle X(t)\right\rangle =0$ and correlation $\left\langle X(t)X(0) \right\rangle \propto e^{-t/\...
1
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0answers
22 views

Consistency of sample quantile to population quantile for discrete variables [closed]

Can I know if the sample quantile converges to the population quantile in probability for discrete variables? If we use Hoeffding (1963)'s results, is this true?
3
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1answer
76 views

Evaluating expected improvement in Mathematica

There is a concept in optimization called expected improvement where you sequentially search for the value of x that optimizes the problem. Here is a screen shot of the general idea of the derivation: ...
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0answers
64 views

Solving $E[abXab]=Y$ for Gaussian $(a,b)$

I have $d/2$-dimensional variables $a,b$ jointly distributed as Gaussian($\mu,\Sigma$) in $d$ dimensions, and need to solve the following equation for $X$ $$E[ab^TXab^T]=Y$$ This is equivalent to ...
0
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1answer
55 views

Defining a Gaussian mixture distribution for $N$ number of Gaussian distributions

I am experimenting a bit with mixed-Gaussian distributions. If I want to define a mixture of two or three distributions, I do this with: ...
2
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1answer
152 views

Raising the normal distribution curve to a specified height on the $y$-axis

I'd like to know how to fit the normal distribution curve between $x$ and $y$ values so that the curve maintains its bell shape. I guessed the sigma is the scale ratio, but it doesn't work as I ...
0
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1answer
91 views

Find the probability (relative volume) of a certain 4-ball with respect to Hilbert-Schmidt measure

Let us consider the set of points {x,y,z,1-x-y-z} and impose the strict ordering constraint ...
0
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1answer
82 views

How to solve the Summation equation by FindRoots [closed]

I want to find out the value of alpha and lambda where u lies between 0 and 1.
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2answers
50 views

using exponential distribution to solve a half life problem [closed]

i have information about the half life of a certain element. the half life is 29 years. i need to calculate how much of this material is left if we start counting from 1954, which was 66 years ago. i ...
-3
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1answer
106 views
2
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1answer
81 views

trying to solve for mean and standard deviation using Normcumdist and Solve [closed]

I am trying to find values for the mean and standard deviation of a normal distribution with these characteristics. $\qquad P(X \le 90) = 0.96$ $\qquad P(X \le 50) = 0.3$ I am trying to do this using <...
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0answers
45 views

Find custom distribution parameters that best fit the PDF/CDF data histograms [duplicate]

I have the probability and cummulative density histograms of some data. I need to find the parameters of a custom distribution that best fit the data. For probability distributions included in ...
0
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0answers
41 views

Performance inconsistency: What's going on here?

Consider: ...
1
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1answer
66 views

How to test if NonlinearModelFit parameters are different from each other

I'm using NonlinearModelFit to fit 5 parameters to some data points and the "ParameterConfidenceIntervalTable" gives ...
0
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2answers
57 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: ...
0
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1answer
69 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 ...
2
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0answers
43 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: ...
2
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3answers
104 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 ...
1
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1answer
123 views

Fisher information for a Gaussian [closed]

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, \...
0
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1answer
51 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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