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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28 views

Calculate dependent probabilities [on hold]

Imagine that two raffles will happen, every raffle will reward 1 person. 10 people will participate. The first raffle will reward 1 person. The second raffle will reward another person, but the ...
2
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1answer
60 views

How do I define a random variable involving Part?

I need to define a random variable that involves Part, but when I try, for example ...
0
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0answers
11 views

Probability clarification [migrated]

Consider the reading habits of the X class. If we know that 30% of the class students read USA Today daily, 40% read Salt Lake Tribune daily and 10% read both of them daily, what is the percentage of ...
8
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1answer
171 views
0
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0answers
167 views

Why does my calculation of a probability take too much time?

I am calculating the value of the following function for given argument values: ...
3
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2answers
75 views

Efficient Sampling of A (Countable) Discrete Distribution

I have a sequence of positive terms $(a_n)$, for which $\sum_{n=1}^\infty a_n = A <\infty$, and wish to take a psuedo-random sample from the discrete probability distribution \begin{equation} ...
2
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1answer
114 views
4
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1answer
53 views
-1
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1answer
54 views

rolling a sum of 6 or less, on 3 dice [closed]

What is the probability of rolling a sum of 6 or less when rolling 3 dice(six sided) at once. I understand how to get the probability of rolling the sum of 6 but of 6 or less confuses me.
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1answer
92 views

Solve ${\rm BinomialDistribution}(x;\,n_1,\,p_1) = {\rm BinomialDistribution}(a-x;\,n_2,\,p_2)$ in terms of $x$ [closed]

I'm totally a novice with Wolfram software, so please forgive me if the question is nonsense. I want to solve the following equation in terms of $x$: $\quad \quad {\rm ...
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2answers
104 views

Simulation of LogNormal process for an asset pricing

I'm new to Mathematica programming, so forgive my rather unsophisticated question. I need to simulate 5000 "walks" of a process value (of a stock) that starts from its current value, at ...
0
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1answer
118 views

Conditional probability

I am new to Mathematica. I am asking how to define a conditinal probability in Mathematica. Here is an example of what I want to do: Assume that $P(x_b\,|\,x_i)=\left\{ \begin{array}{} ...
1
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1answer
69 views

Mean of inverse probability distribution does not agree with explicit integral

I tried to work with the inverse exponential distribution and encountered the following, which I think is an inconsistency in Mathematica (version 10.0.2): ...
6
votes
2answers
270 views

Find fit of an experimental PDF

After quite some struggle, I managed to put up a code that is syntaxically correct. The goal is to find the parameters for a gamma distribution that best match experimental data. The data is a set of ...
2
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1answer
84 views

how to calculate the covariance of sample central moments

$\bar{x}= \sum_{i=1} ^{n} \frac{1}{n}x_{i}$ $m_1=\sum _{i=1} ^{n} \frac{1}{n} (x_{i}-\bar{x})$ $m_2=\sum _{i=1} ^{n} \frac{1}{n} (x_{i}-\bar{x})^2 $ $m_3=\sum _{i=1} ^{n} ...
2
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0answers
51 views

Optimization of custom probability distibutions?

Consider the two tests: Timing[Do[RandomVariate[NormalDistribution[0.5, 0.3]], {200}]] {0.001188, Null} ...
3
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2answers
178 views

Plot contours for 3d histograms

I have a data set which is a list of pairs. From this I can easily make a 3d histogram with Histogram3D[data] or a smoothed ...
1
vote
1answer
66 views

calculate variance of conditional sum of Normals

Let $\quad W \sim N(\mu_0, \sigma_0^2), \quad X_1 \sim N(\mu_1, \sigma_1^2), \quad X_2 \sim N(\mu_2, \sigma_2^2)$ denote independent random variables, and let $c$ denote a constant. I want to find ...
4
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2answers
148 views

Deriving a Rayleigh distribution

When I tried to find this Rayleigh distribution Mathematica couldn't come with an answer: ...
0
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0answers
59 views

How to Fit a Generalized Pareto Distribution to data in Mathematica

I'd like to know how to fit a Generalized Pareto distribution in Mathematica to implement the Peak Over Threshold method for tail estimation of operational risk losses. Does anybody have a toy example ...
2
votes
1answer
76 views

Find confidence interval for negative binomial using Mathematica

I would like to find the exact 95% confidence intervals on the mean of a negative binomial random variable using Mathematica. It is possible to approximate the distribution using a gamma/normal, but ...
4
votes
1answer
70 views

How to get probabilities for multinomial & hypergeometric distribution ranges more quickly?

I often need to calculate the probability of a result from a multinomial distribution falling within some range, e.g., the maximum of the categories having an upper bound, or a lower bound for the ...
9
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2answers
123 views

Why are Binormal and Multinormal giving me different results when I use NExpectation?

fixed in 10.1 (windows) Binormal and Multinormal can both be used to represent normal random variables: ...
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0answers
89 views

Extrapolation of area for a 2D integration

I have a set of points distributed almost uniformly in a certain area of a 2D plane as follow: An example of data points (orange) data = {{0.919443, 1.68921*10^-22}, {0.262277, ...
2
votes
1answer
98 views

Calculate exact Probability of product of normal random variables

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Normal Distribution having location parameter $\mu_{10\times 1} = ...
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2answers
42 views

Simulate from an AR(1) process where the parameters vary over time

I would like to simulate from an AR(1) process, where the $\rho$ parameter in the process of the form: $X_t = \rho X_{t-1} + \epsilon_t$ varies over time. The path of $\rho$ and $var(\epsilon_t)$ ...
1
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1answer
67 views

Find maximum Log likelihood for repeated random variates

I have the following code ...
2
votes
2answers
129 views

How to plot points with error circles on map with latitude/longitude grid

I am currently working on a project to model the location of icebergs in the northwest atlantic. When an iceberg is sighted, an error circle is plotted around it (with a bivariate normal probability ...
2
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1answer
59 views

Why is RandomVariate of special probability distribution doesn't working in all cases

I would like to generate a random variates in Mathematica 9 with this distribution: ...
1
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1answer
73 views

Cannot evaluate TransformedDistribution for vectorial sum

I'm trying to obtain the distribution of the magnitude (length) of the vectorial sum of two vectors under a random (uniformly distributed) angle $\phi$. The sum is $\sqrt{x^2+y^2+2xy\cos(\phi)}$, ...
2
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0answers
113 views

Computational Bayesian analysis in Mathematica: Any plans to develop MCMC?

Does anyone know if there are any plans to develop an MCMC capability in Mathematica? My reasoning for asking is that as it stands, I can't seem to find any 'out-of-the-box' functions/capabilities ...
1
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0answers
86 views

Von Neumann's method to generate points uniformly distributed on a region of a n-sphere surface

I am trying to generate points uniformly distributed on a region of a single n-sphere surface (all angles in hyperspheric coordinates are between 0 and Pi/2). I decided to use von Neumann's method ...
2
votes
1answer
89 views

Time inhomogeneous Markov Chain in Mathematica

I would like to create a discrete 2-state Markov process, where the switching probabilities in the transition matrix vary with time. I can currently do the following, which creates a process with ...
0
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1answer
117 views

how to scale the plot of PDF (t-distribution)

The directions in my book say: "To sketch the t distribution in Figure 3.11, simply multiply the abscissa t value by the scale factor and plot this against the ordinate of t at that point." So ...
4
votes
2answers
208 views

Calculate PDF and CDF of a product of independent exponentially distributed random variables

Let x[1], x[2], ..., x[n] be independent random variables each of which is distributed exponentially, i.e. with the PDF ...
0
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1answer
74 views

Sketch Probability density function [closed]

My question is : Suppose that the PDF of a random variable X is as follows: \begin{equation*} f(x) = \begin{cases} ce^{-2x} & \text {$x > 0$}\\ 0 & \text {otherwise}\\ ...
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2answers
77 views

Maximum likelihood estimation based on frequency table

I have a frequency table of grades, I'm trying to estimate the distribution as a truncated normal distribution (a grade below 65 is a failing grade and doesn't count). Since I don't have the actual ...
1
vote
1answer
98 views

Mean Preserving PDF Spreading

I have a histogram representing the PDF (probability density function) of an unknown discrete RV. The histogram is asymmetrical. Is there a known way in Mathematica to increase/decrease the variance ...
7
votes
2answers
488 views

Probability: Calculating a multiple integral

Find the value of $P[\Pi_{i=1}^{10}X_i > C]$ for $C=2,5$, where $X_{10\times 1}$ is a random vector with $10$ dimensional Cauchy Distribution having location parameter $\mu_{10\times 1} = ...
4
votes
2answers
182 views

When analytical and numerical methods do not agree - Case study with Maximum Likelihoods methods

Here is the probability distribution I am interested in: $$P(q)=C e^{4 n s q} q^{4 n \nu - 1} (1 - q)^{4 n \mu - 1}$$ , where $e$ is the constant of Euler and $C$ is constant so that the whole thing ...
1
vote
3answers
195 views

Find 2 points in a normal distribution with these given properties

I would like to find a and b. How should I code this in Mathematica? What I did wrong? ...
2
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0answers
53 views

Help with Multivariate ProbabilityDistribution

I wish to obtain numbers from ...
0
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0answers
86 views

Constrained Nonlinear Optimization with expectations functions in the constraints

I am modeling an optimal compensation contract with a CRRA utility function : ...
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0answers
47 views

Why is Plot3D applied to TransformedDistribution in 2 random variables so slow?

I am trying to plot 3D, the pdf of a TransformedDistribution made up of random variables. So I can see the pdf in 3D, similar to this answer here Visualizing a 2-dimensional PDF But it seems to take ...
1
vote
1answer
46 views

Specifying that hierarchical probability distribution conditional on independent random parameters

I would like to create a ParameterMixtureDistribution to model the following: $X \sim $ Binomial($N,P$) $N \sim \mathrm{Poisson}(\lambda) \perp P \sim ...
0
votes
0answers
39 views

Mixture / Hierarchical Distribution from Conditional

How does Mathematica handle Hierarchical distributions. For example, if I have X|Y ~ Poisson(Z) Y ~ Exp(lambda) Z ~ Normal(0,1) First, of all, the distribution of X is only given conditionally and ...
0
votes
1answer
79 views

probability calculation with two independent normal RVs

I don't understand why Probability[X < Y, {X \[Distributed] NormalDistribution[0, 1], Y \[Distributed] NormalDistribution[0, 1]}] gives 1/2 while we know ...
1
vote
1answer
75 views

Find a probability with random variates from the same distribution

I'm trying to find Probability involving 3 random variates from the same distribution, but Mathematica does not seem to solve it. ...
0
votes
1answer
50 views

Central Limit Theorem - solve for a const, given probability

I hope this is not a very complicated question, but I have problems finding the answer. Quite often, I need to calculate something like this: $P(-a<\bar{x}<a) = p$, where $\bar{x}$ refers to the ...