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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0
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1answer
59 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
112 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: ...
4
votes
1answer
81 views

Define customised distribution with discontinuous CDF

I have the following CDF: ...
0
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0answers
97 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 ...
0
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0answers
43 views

Using an Interpolating Function as a probability density function [duplicate]

I have seen a couple of similar questions but have not been able to figure out a solution for my particular problem. I have a probability density function of two variables ...
1
vote
1answer
107 views

Summing Normal random variables

I would like to plot the graph of the sum of two random variables.So, I wrote Plot[PDF[NormalDistribution[0, 1]+NormalDistribution[0, 1], x], {x, -10, 10}] Why ...
1
vote
1answer
176 views

2D Markov Process

I have a homework project. I need to analyse a gambler's ruin where there are 6 possible outcomes of every wager with corresponding probabilities and payoffs and the gambler may vary the wager (say ...
1
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0answers
232 views

When are `If`, `Piecewise`, `Switch`, and `Which` interchangeable and when are they not?

Experimenting with joint dependent distributions via the TransformedDistribution function, I used the following to derive a distribution where the second variate is ...
1
vote
1answer
230 views

Detecting a nonlinear edge in a 2D point pattern

Following an earlier post here, I have generated a point pattern on the unit square $[0,1]\otimes[0,1]$, which is described by a piecewise constant intensity function constructed so that (in ...
1
vote
3answers
405 views

Generate random points in a region with higher probability in a sub-region

I am trying to generate random samples of points in the unit square in such a way that points inside a given circle are twice as likely to be selected as points outside that circle. I tried to ...
1
vote
2answers
168 views

Analyzing Betting (Keno) in Mathematica [closed]

Keno is a popular lottery game that is available with all of the larger casino softwares. The player is given a ticket with 70 numbers on it. He picks 1 to 11 numbers on the ticket. 20 winning numbers ...
7
votes
1answer
129 views

How to create a spliced survival statistical distribution?

I am trying to use Mathematica for more of my reliability engineering work and am having trouble using SplicedDistribution. I have a Weibull distribution (dist1) associated with a low stress ...
2
votes
1answer
176 views

Making a histogram of a user defined random variable

Suppose I want to generate a histogram of $n$ trials a slightly complicated random variable in Mathematica. Is there an easy way to do this? For instance, to make a histogram of a normal variable one ...
0
votes
1answer
97 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
votes
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: ...
4
votes
2answers
321 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
votes
2answers
133 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
83 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
204 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
330 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
votes
0answers
124 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
votes
4answers
104 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 ...
7
votes
1answer
149 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
votes
0answers
171 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
votes
4answers
132 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
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1answer
328 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
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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
52 views
0
votes
1answer
132 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
205 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
134 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
424 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
votes
1answer
229 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
496 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
139 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
205 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
126 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
151 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
759 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
272 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
137 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
191 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
528 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
465 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
votes
0answers
196 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 ...