Questions about performing probabilistic calculations, especially those concerned with the Mathematica commands Probability, Expectation and the various functions related to distributions such as NormalDistribution, CDF, PDF etc.

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6
votes
4answers
205 views
2
votes
1answer
55 views

FindDistributionParameters of a sum of a mixture distribution

I have this Mixture Distribution of two Normal Distributions: ...
0
votes
1answer
55 views

Inclusion-Exclusion Principle Implementation

I would like to know how I can write a Mathematica code for the Inclusion–exclusion principle. The formulas governing it are: $ P(\bigcup_{i=1}^n A_i)=\sum_{k=1}^n (-1)^{k-1} ...
3
votes
1answer
73 views
1
vote
0answers
19 views

Sum of truncated normal random variable and normal random variable [migrated]

I'm wondering if there is a closed-form pdf of sum of "correlated" normal random variable and truncated normal random variable. I found a paper providing the pdf for "uncorrelated" case, but could ...
18
votes
2answers
268 views

Negative probability?

I am trying to get the sum of the squares of seven random variables, all uniformly distributed. This is what I tried. ...
0
votes
0answers
16 views

Explain how assigning n tasks to n persons randomly gives a sample space of n^n? [migrated]

I was studying linearity of expectation topic and there was an example of assigning n processes to n different servers randomly, as per i can think - 1st process to any of n servers so "n" ways, 2nd ...
0
votes
0answers
81 views

How to be faster at making a frequency list of increasing steps

I want to find propabilities of having a sequence in a list, by using frequencies. The case is that you will bet on an increase when the last event had an increased and bet on derease when the last ...
2
votes
2answers
94 views

Finding Expectation of function of a Log-normal distribution

Say $Y=g(X)$ and $p_X = \frac{e^{-\frac{(\mu -\log (x))^2}{2 \sigma ^2}}}{\sqrt{2 \pi } x \sigma }$ is Log-normal density function: [Wiki] Find E[Y]? Since $E[Y] = \int_0^\infty y f_Y \ dy = ...
0
votes
1answer
50 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 ...
5
votes
0answers
139 views

Calculating probabilities symbolically

Is there a way to solve for statistical quantities analytically/symbolically in Mathematica? example 1: Lets say that I want to do a calculation that requires Bayes theorem. I know p(a), p(b) and ...
0
votes
1answer
454 views

PDF of binomial distribution and mixed binomial distribution

I want to plot the PDF of binomial distributed function and a mixed binomial distributed function, therefore I entered for the binomial distribution function the following: ...
4
votes
3answers
222 views

Function given exact arguments returns hugely different value than it returns when given equivalent inexact arguments

I was trying to compute the probability that a coin is from a particular underlying distribution given that a particular set of tosses was observed. (I know this can be done in a different way, but I ...
0
votes
1answer
78 views

Generating a list of standard normal random variables

Im trying to generate a list of random (standard) independent normal variables. For this, I first generate a random list of, say, 100 real numbers in the range [0, 1000], and then make them standard ...
6
votes
1answer
94 views

Why am I getting wildly incorrect results from FirstPassageTimeDistribution with inexact transition matrix?

Working on some large systems using DiscreteMarkovProcess, I changed the transition matrix to machine precision vs using exact values, which sped things up handily. ...
5
votes
1answer
292 views

Is there a free version of the Springer book “Mathematical Statistics with Mathematica”?

Is there a free version of the Springer book: $$\text{Mathematical Statistics with Mathematica}$$ by Rose and Smith ... available on the internet?
0
votes
0answers
46 views

Expectation taking unusually long to evaluate

I am trying to evaluate an expectation, but it is taking an extremely long time although the expression itself should not be too complicated. My code is ...
0
votes
0answers
39 views

Symbolic manipulation of the moments of an unknown distribution

I'm curious as to whether it's possible to get Mathematica to simplify/manipulate/expand basic expectations, conditional expectations, sums of random variables, etc. A simple example might be: ...
0
votes
0answers
28 views

Chi square: compare two different distribution

I try to compare two file with two different distribution of numbers. So i have random1.dat and random2.dat each one are vectors of more then 1000 rows. I saw from this question Doing a chi-square ...
13
votes
2answers
975 views

Obtaining joint distributions and conditional distributions using Mathematica

I have two multivariate Gaussian distributions $p(x)$ and $p(z)$ with mean vectors $m_x$ and $m_z$, and covariance matrices $\Sigma_x$ and $\Sigma_z$. my model is a simple linear model $x = W z+n$ ...
2
votes
1answer
174 views

Reversing Autocorrect, aka how to find the word that was supposed to be there

When I receive messages from people using their smartphones I usually see typos and, worst, typos corrected by Autocorrect. Now, I receive messages in English, which is not my first language. I can ...
3
votes
2answers
100 views

Calculating the conditional probability of discrete samples

I have two lists: a = {0, 1, 1, 1, 0, 1} b = {1, 0, 1, 1, 0, 0} I'd like to calculate the conditional probability of a given b; for example, $p(a=1 | b=0)$. Is ...
10
votes
4answers
506 views

How do I solve this probability problem with Probability?

Consider a stick of length 1. Pick two points uniformly at random on the stick, and break the stick at those points. What is the probability that the three segments obtained in this way form a ...
0
votes
1answer
60 views

Working with means and variances

My goal is to work out on the following equation: $$Mean(P)(1-Mean (P))\left (h + (1 - 2 h) (1 - \frac {Var (P)} {Mean (P) (1 - Mean (P))}) (1 - Mean (P)) + \frac {Var (P)} {Mean (P) (1 - Mean ...
1
vote
1answer
92 views

Bilateral Laplace Transform in Mathematica (to be used with Moment Generating Functions)?

I am trying to solve a linear ODE for a Kolmogorov forward equation to get a stationary distribution of a random variable. The easiest approach may be to transform the ODE with a two-sided Laplace ...
0
votes
0answers
38 views

Time varying Poisson rate using ParameterMixtureDistribution

I have a system in which there is a Poisson arrival process with rate $\lambda$. I need to split this process into two independent poisson processes $\lambda_i$ and $\lambda_u$. Where ...
2
votes
3answers
267 views

How do I plot two Gaussians/normal distributions with 2 different means and 2 different standard deviations?

This is probably very easy for someone with more experience, but I am trying to plot only two Normal distributions, but for some reason my Method plots 4, instead of 2. I have: ...
5
votes
1answer
95 views

MarginalDistribution with Symbolic range in ProbabilityDistribution

Given the following joint density: for 10 < x < 20, x/2 < y < x. To find the marginal density for X we do: ...
1
vote
1answer
84 views

Expressing a joint distribution for use in ContourPlot

I have $$X_1=T + W$$ $$X_2=2 T + 3 W$$ where $$W \sim N(3,5) \,\text{;}\,\, T \sim N(1,2)$$ and $$P(X=X_1)=P(X=X_2)=\tfrac{1}{2}$$ which I have awkwardly expressed as ...
3
votes
1answer
137 views

Determining the dimension of a probability distribution

Functions like Mean and RandomVariate clearly infer the dimension of the distribution passed to them. One can also usually ...
0
votes
1answer
62 views

Pattern matching with PDF, Distributed and multivariate distributions

I have defined a function to compute the Shannon entropy of a probability distribution: ent[p_] := Expectation[-Log[PDF[p, x]], x \[Distributed] p] This works ...
1
vote
0answers
50 views

An example of how to compute numerically the KL-divergence in mathematica [closed]

I wanted to compute an exact number for two probabilities that I am comparing. These are two normal distributions as: $$Normal(\mu = 5, \sigma = 4)$$ $$Normal(\mu = 5, \sigma = 5)$$ I decided to ...
3
votes
0answers
111 views

What can I do to improve the performance of my calculations?

I'm trying to express a simple probability problem in Mathematica, but am having trouble getting my calculations to execute at a reasonable speed. I have an object whose unknown location is modeled ...
3
votes
1answer
177 views

Put random points into a specific 2D subregion

I want to cover a particular subregion of the x-y plane with a random distribution. As this particular region is not a circle I encounter some problems declaring the permitted zone where to put ...
0
votes
0answers
84 views

Constrained maximum likelihood

Trying to solve a MLE with nonlinear constraints that need to be satisfied. However, the given solution do not match the constraints. Am I doing it correctly? ...
1
vote
1answer
91 views

Difficulty finding Expectation of a special function

I have a special function given as: $${\rm f}\left(r\right) ={1 \over \beta\lambda}\,2^{r/\beta} \exp\left({\left[2^{r/\beta} - 1\right]K \over \lambda}\right)$$ I should find the Expectation of ...
16
votes
2answers
734 views

How to compute the inverse CDF properly?

Note: this has been fixed in version 9. I want to compute the CDF and inverse CDF of the hyperbolic distribution: ...
12
votes
1answer
169 views

NExpectation behaves oddly with EmpiricalDistribution

Note: this is fixed in version 9. My question concerns the usage of NExpectation and Expectation and why I see the behavior I ...
3
votes
0answers
72 views

Converting problem into form involving Probability

I want to solve the following problem symbolically, using Probability: What is the probability of the first random variate of a set to be present more than ...
1
vote
0answers
126 views

Slow mixture fitting when having ill-conditioned covariance matrices. How to make it faster?

I'm using Mathematica 9.0 to fit multidimensional observations with a gaussian mixture. To do so I first adapted these steps to ensure that the mixture parameters are well defined (see ...
3
votes
1answer
76 views

Where do Mathematica's probability functions draw a line in the sand for predicates?

Thinking about a recent question mis-posted here (belonged on math), I noted the following. A contrived example - probability that a or b are 1: ...
3
votes
1answer
194 views

Categorical Distribution

Suppose I want to do calculations with a random variable $X$ that has a simple categorical distribution (a.k.a generalised Bernoulli distribution or discrete distribution). I was expecting to be able ...
0
votes
0answers
95 views

Probability Model

I have the following probability model: $(X_k|\text{ PastHistory}_{k-1}, \theta_0, \theta_1, \theta_2) \sim (\pi\cdot N(\theta_1+\theta_0\cdot X_{k-1},1)+(1-\pi)\cdot N(\theta_2+\theta_0\cdot ...
1
vote
1answer
71 views

How to define an n-variate empirical distribution function probability for any n?

I'm using Mathematica 9.0 to calculate the probability according to the empirical distribution function (EDF) of some sample data. Afterwords this is included in a maximization stage so I define this ...
2
votes
1answer
83 views

Define shifted pdf

I defined a PDF called dist, for example like this one: ...
0
votes
1answer
56 views

Calculate expected value of custom pdf

I've a custom pdf in the sense that it's the convolution of several other PDFs p[t_] := Convolve[p1[x],p2[x],x,t]; Now I want to calculate the expected value of ...
0
votes
1answer
109 views

PDF for Gamma Distribution not what I expect

I have plotted the the PDF for a Gamma Distribution with various parameters (e.g. 3 and 5) using Manipulate: ...
28
votes
6answers
2k views

Efficient way to generate random points with a predefined lower bound on their pairwise Euclidean distance

Using Mathematica what is an efficient way to generate a list of $n$ random two dimensional points $\{x_i,y_i\}$ where $i=1,...,n$ so that no two points $p_1$ and $p_2$ in the list has an Euclidean ...
4
votes
1answer
78 views