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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1answer
92 views

How can I type "aprox symbol in Mathematica? [closed]

I want to obtain a value of the Normal Distribution, but I can´t type "approx symbol" before Normal Distribution" to tell Mathematica that x FOLLOWS N[0,1] How can I do it? Probability[z >= 8.49, z ...
0
votes
1answer
72 views

Find the point that holds a given property

I have a normal distribution with mean 106, and a standard deviation of 8. I'm being asked to find the point that has the property that 25% of these values have this value or lower. What I've ...
0
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1answer
184 views

Solve Probability of Distribution

Why does this work: Solve[Probability[x <= t, x \[Distributed] NormalDistribution[]] == 0.95 ,t] But this doesn't: ...
1
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1answer
248 views

Why does this integral have a complex component?

I wanted to find the probability of my normally-distributed random variable being at least 15, so I set up this integral: ...
4
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2answers
130 views

Finding the characteristic function of a TransformedDistribution[]

I am trying to find the characteristic function of a sum of "named" distributions, though I am interested in how to use Mathematica to find the characteristic function of $$f(X_1,\ldots, X_n),$$ where ...
1
vote
1answer
81 views

How to use ProbabilityDistribution for a posterior expression [duplicate]

I am performing a Bayesian updating on a Lognormal prior. After combining the prior and likelihood and dividing by the normalization constant I get the following expression as the posterior: ...
1
vote
2answers
201 views

How to use Mathematica in my Problem as I would use it in Matlab

I would like to calculate the convolution of a function with itself for $n$ times. Let $n$ be $10$. For $n=1$, I wont make any calculation and $f0$ is my function, when $n=2$, I will convolve $f0$ ...
4
votes
3answers
326 views

Plotting the convolution of the same probability density function with itself

I would like to compute the integral $$q_n(x)=\int_{B}^A q_{n-1} (\omega)f(x-\omega)\mathrm{d} \omega,\quad q_1=f,\quad n\geq 1.$$ for a given density function $f$. Basically it is the convolution ...
0
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0answers
122 views

Discrete distribution binomial set up

I hope one of you guys can help me out. I am trying to visualize a discrete distribution based on a binomial distribution and a mixed binomial distribution. In the first step I started to determine ...
3
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4answers
102 views

Check whether a function of two variables is a probabilty distribution function

I have a function like this $f(x,y)=c\,y\,(y-x),\ \text{for}\ 0<x<2,\;-x<y<x$ and I need to find the value of $c$ such that $f(x,y)$ is a PDF. How can I do that? I know that the ...
6
votes
1answer
141 views

RandomVariate does not fill range of PDF of distribution

I've declared my own probability distribution as follows dist[a_, b_] := ProbabilityDistribution[Cos[(b x)/2]^2 Sinc[a x]^2, {x, -400, 400}]; When I try to ...
3
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0answers
164 views

Markov Chain for combined events?

I was wondering how to apply Markov steady-state chains to a simple case in genetics, eye colour. Assuming the probabilities of being brown, green or blue eyed, given your parents were a certain ...
4
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4answers
129 views

How do I emulate DiscreteUniformDistribution in Mathematica?

How do I define a function from scratch that emulates DiscreteUniformDistribution? As shown below, attempting to use ...
0
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0answers
48 views

Determine appropriate initial conditions for exit time

These are some constants: ...
1
vote
1answer
322 views

How to compute the Multifractal Spectrum of a Financial Series with WTMM

I would like to know if someone knows how to compute the Multifractal Spectrum of a Financial Time Series (Currency) througth the Wavelet Transformation Modulus Maxima (WTMM). I would highly ...
0
votes
0answers
51 views

Identify columns of a huge matrix just polynomially many rows chosen at random

I am interested in the following problem in combinatorics $\Cap$ Probability. Let $\lambda \in \mathbb{N}$ be a parameter. Consider a matrix of $2^\lambda$ rows and $2^\lambda$ columns. Each column ...
1
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1answer
51 views
0
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1answer
129 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
198 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
131 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
416 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 ...
12
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1answer
218 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
453 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
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1answer
137 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
200 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
125 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
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1answer
145 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
719 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
261 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
177 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
128 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
186 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
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0answers
522 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
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0answers
91 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
143 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
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3answers
446 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 ...
5
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0answers
193 views

Speeding up multilinear PRA branch-and-bound algorithm with worst-case exponential time scenario with respect to basic events

The algorithm is a branch-and-bound algorithm that calculates dominances for PRA, probalistic risk assessment. The task was to find faster ways to do it in numerical software such as Matlab but we ...
3
votes
4answers
214 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
705 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
762 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
502 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
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3answers
547 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
909 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
192 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
201 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
262 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
161 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 ...
6
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1answer
786 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
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1answer
536 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 ...