Tagged Questions

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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1
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1answer
52 views
0
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1answer
138 views

Convert probability example to a distribution

Consider a box which contains 30 balls. 10 red, 10 white and 10 blue balls. There will be picked 4 balls randomly, without putting the balls back to the experiment. My question is: How do I create a ...
2
votes
1answer
216 views

Compute Correlation between two binary variables

$X_1$ and $X_2$ are two binary stochastic variables with simultaneous probabilitydistribution: $$ \begin{matrix} &X_2=0&X_2=1\\ X_1=0&0.30&0.17\\ X_1=1&0.08&0.45 ...
2
votes
2answers
138 views

Conditioned Probability Task

I have this task with two questions I would like to compute in Mathematica. Suppose a pair of random variables $(X, Y)$ has a equal distribution on the following 7 points: $\begin{matrix} ...
6
votes
3answers
454 views

Calculate probability function

I would like to calculate the following with Mathematica: Let $X$ be a random variable with probability function $$p(x)= \left\{ \begin{matrix} \frac{x}{6} & \text{for }x \in \{1,2,3\}\\ 0 ...
13
votes
1answer
246 views

Randomness test suites that can be invoked from Mathematica

There are several test suites referenced at csrc.nist.gov designed to test a (pseudo-)random byte sequence for randomness, and discover possible skews, correlations, patterns, or other hidden ...
0
votes
1answer
551 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: ...
0
votes
1answer
147 views

plot probability

Hi I just want to flatten a function, I tied it with Joined->True, but it did not work, hope somebody of you can help me. This is my code: ...
2
votes
1answer
214 views

Expectation function does evaluate my expression

I am trying to evaluate the expression Expectation[(B x (-6 b + 12 a n0 + B x + B^2 x^2))/(2 (6 a + B x + B^2 x^2)), Distributed[x, BetaDistribution[α, β]]] ...
0
votes
0answers
127 views

My algorithm produces too many permutations

Imagine the following problem. A population of size $n$ consists of $i$ men and $n-i$ women. The population goes to the casino. Call $g_m$ ,$g_w$ the amount of money won by men and women respectively. ...
0
votes
1answer
156 views

How to simulate with a user specified bivariate continuous probability distribution [duplicate]

I am very new to Mathematica set up and I have the following question: I have a bivariate probability distribution which is a little complicated and of the form: $$f(x,y)=(a_0+a_1+a_2)\frac{a_1 ...
8
votes
1answer
825 views

Mathematica code for hidden Markov models (HMM)

I am looking for some simple Mathematica code to model an HMM with just a few states and an equal number of observable signals (emissions). I am hoping to generate sample paths and keep track of the ...
2
votes
3answers
290 views

Covariance of transformed random variables

I am trying to solve the following: $\begin{align*} &X \sim N(1,1)\\ &\mathrm{cov}(X, X^3) = \text{?} \end{align*}$ where $\mathrm{cov}$ is the covariance. How would you do this in ...
2
votes
2answers
179 views

Stochastic problem

I have to organize a small sports league and I am puzzled on how to create the game plan. We are 8 persons playing table soccer with 2 vs. 2 matches. The idea is that each person plays once with ...
0
votes
0answers
142 views

Plotting a mixture CDF with a truncated distribution in version 7

I'd like to plot the CDF of the following pdf in Mathematica 7: $$f(x)=0.1 g(x)+0.85 m(x)+0.05 h(x)$$ where $$ \begin{array}{ccl} g(x)&:&P(0)=1,\ P(x\neq 0)=0\\ ...
1
vote
1answer
195 views

Safe values of $\mu$ and $\sigma$ when randomly sampling from a Log-Normal Distribution?

I believe I'm obtaining overflow errors when randomly sampling from a log-normal distribution with the command: RandomVariate[LogNormalDistribution[μ, σ], 1] ...
2
votes
0answers
553 views

Calculate variance of random walk?

How can I symbolically calculate the variance of the following random walk in Mathematica? Given several discrete random variables such that $p(Z_i=1-2k)=p$, where $k$ is a small real number, and ...
3
votes
0answers
93 views

shortest paths in probabilistically weighted edges? [duplicate]

I understand Mathematica can find shortest paths. However, is it also able to find the most probable paths? I mean this is a case where edges are given probabilistic wights (from 0 to 1) and the most ...
4
votes
1answer
145 views

Combinations which do not have elements in common

I can choose 2 letters from the four letters $\{A,B,C,D\}$ in 6 combinations using the combination formula $$\frac{n!}{ r! (n-r)!}$$ ...
12
votes
3answers
476 views

Simulate a simple spinner

I'm teaching some simple ideas in probability to students in grade 7. The "spinner" below works, but I'm wondering how I could make it just a bit more realistic by having it actually "spin" around a ...
6
votes
1answer
234 views

Speeding up the non-negativity algorithm for multilinear function with interval probabilities?

The algorithm is a branch-and-bound algorithm that calculates the non-negativity of a multilinear function with interval probabilities. The lines 9-11 has an optimization that is explained on the ...
3
votes
4answers
220 views

Descriptive statistics of two events

I am trying to use the descriptive statistics feature of Mathematica to answer the following question: suppose I have two events, A and B, whose occurrence is described by a normal distribution around ...
0
votes
1answer
769 views

Solving derivative of cumulative normal distribution log likelihood

I am a newbie and I'm trying to use Mathematica to obtain the symbolic Maximum Likelihood Estimation for a cumulative normal distribution. So far I have reached the step where I have the derivative of ...
3
votes
2answers
868 views

Empirical Cumulative Distribution Function

I have a data set of the form $d=\{(y_1,x_1),(y_2,x_2)...(y_n,x_n)\}$ for a large $n$. A non-parametric plot of this data (a scatter plot where all observations are sorted along $x$ and joined with a ...
10
votes
4answers
532 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 ...
1
vote
1answer
120 views

PDF on TransformedDistribution of two BinomialDistribution too slow

I'd been doing my own convolutions of distributions for some calculations, decided to use built-ins. With ...
4
votes
3answers
612 views

Graphical Plots of PDF and CDF

I have a joint density and distribution function that I want to plot in a meaningful way, (i.e., want to be able to see how the functions behaves as changes in x and y happen simultaneously. If ...
16
votes
3answers
960 views

What is the average of rolling two dice and only taking the value of the higher dice roll?

I am referencing to this question on mathunderflow: What is the average of rolling two dice and only taking the value of the higher dice roll? Now I tried: ...
2
votes
1answer
198 views

My Data has negative and positive numbers, can I still use it to get the PDF?

I have data that reflects the arrival time of a flight. {3, -2, 16, 13, -6, 5, 4, -7, 7, 0……..n} this is for 8:45am and has 150 elements "arrivals" The positive values represent the time in minutes ...
4
votes
1answer
204 views

Reproducing a graphic on Jensen's inequality for the probabilistic case

I am trying to reproduce the following graph on Jensen's inequality for the probabilistic case (source: wikipedia) but with the exponential function as Y, the normal distribution on the X-axis and ...
-4
votes
2answers
277 views

Calculate one-tailed critical point from a probability distribution

I would like to calculate the numerical value of $\xi\in\mathbb{R}_{\geq0}$$$P(|U|<\xi)=0.95$$ where $U$ is standard-normal distributed. How may I do that in Mathematica?
4
votes
1answer
167 views

Expectation of CauchyDistribution

I've noticed this strange behavior and I'm wondering if it's a bug. I define a Cauchy distribution: c = CauchyDistribution[0, 1]; If I evaluate ...
9
votes
2answers
908 views

Mathematica Package for Bayesian Networks

Are there any packages that allow the simulation of Bayesian Networks with Mathematica? I found what seemed to be a promising package (Dynamics) on a Brown University URL, ...
8
votes
1answer
565 views

Recommended book on random processes to understand new functionality in Mathematica 9?

I am interested in exploring the new functionality on random processes available in Mathematica 9, but I am not familiar with all of the underlying mathematics. Could you recommend a book that ...
14
votes
1answer
342 views

RandomVariate returns values outside the support of a PDF

Let $X$ be a random variable with pdf: dist = ProbabilityDistribution[1/(Abs[x]*Log[Abs[x]]^2), {x, -E^-2, E^-2}] Here are some pseudo-random drawings from it: ...
0
votes
1answer
240 views

Trying to plot this probability

Can anyone help me plot this? log P(X >= x) = alpha logx x=0.001 + k(0.001) k= 0, ..., 100 I can't figure out the coding for this.. I've been trying this for a while, and can't seem to figure it ...
11
votes
3answers
3k views

How to generate a RandomVariate of a custom distribution?

I'm trying to generate a pseudorandom variate out of a custom distribution. Suppose I want define a custom distribution, and for the sake of simplicity I define a Poisson distribution (the ...
16
votes
2answers
827 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: ...
11
votes
2answers
3k views

How to calculate the mode of a probability distribution

I was wondering if there is any command to get the mode of the probability distributions. Calculating manually, the mode is (alpha-1)/(alpha+beta-2) While the mean, median or variance of the beta ...
5
votes
4answers
319 views

Probability: proportion of 1000 random lists for x that contain the same nrs

Give a function which calculates for each x a random list of birthdays (which can be x=1 to x=365) birthdays[x_] := RandomInteger[{1, 365}, x] is my answer. ...
4
votes
2answers
228 views

How to find the variance under the assumption that x follows some probability distribution

I am aware that we can find the expectation under the assumption that x follows some probability distribution, something like this: ...
5
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1answer
322 views
2
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2answers
446 views

Total Variation Distance of probability matrix

How can I calculate the Total Variation Distance of a transition Matrix? is there any built in function? I've searched all documentation and haven;t found anything. ** More information: Let me try ...
14
votes
2answers
1k 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 $x = W z+n$ ...
7
votes
1answer
980 views

Probability and distribution from actual data

Let's say I have some data from a real world system: ...
8
votes
2answers
541 views

Expected Value: Strange/unexpected result

Assume $X$ is an exponential random variable with unit mean ($f_X(x)=e^{-x}$, $x>0$). I want to calculate the expected value of $\frac{1}{X}$. Since $X>0$, I am expecting that ...
3
votes
0answers
104 views

ProbabilityDistribution PDF on boundary points

I would like to evaluate the PDF of a custom ProbabilityDistribution at the min and max values. However, PDF[...] returns 0 at ...
2
votes
3answers
556 views

Some questions about random numbers

How can I get non-repeating random numbers from Mathematica 8? How can I know which distribution the numbers I get are? Can I choose the distribution I want together with the non-repeating random ...
12
votes
1answer
171 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 ...
0
votes
1answer
312 views

How can an InverseQuantile or an interval valued Quantile function be implemented in Mathematica?

Quantile[] is the workhorse method in robust data analysis and statistics (see, eg Koenker's Quantile Regression). However, it should be complemented by an ...