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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2
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1answer
53 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
47 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
votes
1answer
99 views

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

Binormal and Multinormal can both be used to represent normal random variables: ...
0
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0answers
19 views

What is more probable; one 50 percent chance, or ten 5 percent chances? [migrated]

What is more probable; a single 50% chance at success, or ten 5% chances at success? If the former, how many additional 5% chances are required in order for it to be as likely to succeed using ...
1
vote
0answers
75 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, ...
0
votes
0answers
3 views

Counting probability problem [migrated]

New to probability I am getting stuck on this counting problem Assuming two numbers are selected at random from a black box with replacement from the integer set {1, 2, . . . , n} and let K be the ...
0
votes
0answers
13 views

How to count probability of given numbers? [migrated]

I have these numbers and probabilities: Activity | Probability A | 2.49 B | 3.97 C | 1.27 The lower the probability number is, the more ...
0
votes
0answers
37 views

Tricky Poisson distribution question [migrated]

Am new to probability and have been struggling to solve the following question. Assume X1,...,X4 are IID with Xi ∼ Po(λ). Let Y = 1/4 (X1 + ··· + X4). Find Pr (Y < 2) in terms of lambda. Can ...
1
vote
0answers
58 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} = ...
0
votes
2answers
32 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
vote
1answer
55 views

Find maximum Log likelihood for repeated random variates

I have the following code ...
0
votes
0answers
3 views

Expected value in probability? [migrated]

Isn't the definition of expected value little non mathematical. I mean average is defined when experiment is done, so how can we before hand tell the expected value. Let say for toss, if I get ₹1 for ...
2
votes
2answers
108 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
votes
1answer
50 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
vote
1answer
65 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
votes
0answers
65 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 ...
0
votes
0answers
62 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
68 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
votes
1answer
82 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
179 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
votes
1answer
59 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}\\ ...
1
vote
2answers
57 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
88 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 ...
4
votes
2answers
305 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
168 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
171 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? ...
1
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0answers
46 views

Help with Multivariate ProbabilityDistribution

I wish to obtain numbers from ...
0
votes
0answers
65 views

Constrained Nonlinear Optimization with expectations functions in the constraints

I am modeling an optimal compensation contract with a CRRA utility function : ...
1
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0answers
43 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
37 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
35 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
74 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
58 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
45 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 ...
0
votes
0answers
10 views

In Mathematica, how to calculate marginal probability of continuous conditional distributions? [duplicate]

I have random variables A and B, given by Beta distributions. This can be easily defined in Mathematica. I have a conditional probability P(C|A,B) which I custom-design as a function. The function ...
1
vote
1answer
50 views

There is an higher probability to win with 3 dices versus 2 or with 4 dices versus 3?

In Dice wars, you gain a territory rolling the dices you have in an adiacent territory (almost like Risk game). If I have more options to choose, there are more chances to win with 3 dices versus 2 ...
0
votes
1answer
51 views

probability going outside 1 (due to optimization violation of constraint)

I am working on an optimization, which involves the following density: ...
2
votes
1answer
105 views

How to get a more compact form of this probability calculation?

Inspired by the probability calculation here, I am trying to solve a little general one: $$\mathbb{P} (\sum_{i=1}^{m-1} A_i + \sum_{i=1}^{m} S_i < L < \sum_{i=1}^{m} A_i + \sum_{i=1}^{m+1} ...
2
votes
1answer
59 views

TransformedDistribution using n iid random variables

How do I create a TransformedDistribution that uses $n$ independent identically distributed (i.i.d.) random variables? For example, I can derive a chi-squared ...
4
votes
2answers
232 views

what is The Formula behind the Kolmogorov-Smirnov test statistics?

I calculate the Kolmogrov-samirnov test statistic for the following data: ...
0
votes
1answer
44 views

Combining two SmoothHistogram plots without normalization of each

I'm trying to plot a density of states out of a list of energy values, and on it I want to include another over-layed plot with it that shows some fraction of that density of states at different ...
5
votes
1answer
306 views

How to solve this probability symbolically or numerically?

I am trying to calculate the following probability $$\mathbb{P} \big(\sum_{i=1}^{m} (A_i + S_i) \le L < \sum_{i=1}^{m+1} (A_i + S_i) \big)$$ where, $$A_i \sim \exp(\lambda), \quad S_i \sim ...
2
votes
1answer
150 views

on Kolmogorov-Smirnov test

I found a problem to calculate Kolmogorov-Smirnov test statistic or p-value the data is ...
2
votes
0answers
62 views

Belief Network, Bayesian network

There is already a question about simulating Bayesian networks with Mathematica (Mathematica Package for Bayesian Networks). However, are there any packages or approaches which help in computing the ...
2
votes
1answer
63 views

Statistical Analyzis of Observed Data (Queuing Process)

Basically I have a process that belongs to a certain state at any point of time. However, the time intervals are not fixed (in fact they are exponentially distributed). Essentially, the data points ...
3
votes
2answers
128 views

RandomFunction and Histograms

RandomFunction[QueueingProcess[3, 5], {0, 15}] Histogram[data, Automatic, "PDF"] gives a very nice way to see the histogram based on the specified process. ...
2
votes
0answers
71 views

Simulating Dynamic Priority Queues

I have found several examples of static priority queue implementations: there are two classes of items, with the exponential interarrival times. The service times are also exponential. The first-class ...
0
votes
1answer
40 views

Understanding `TransformedDistribution` behavior on two similar lines of code

The two following lines of code does not give the same output. Mathematica manages to calculate the first one but fails to calculate the second one. ...
1
vote
2answers
137 views

Calculate expected value of piece-wise pdf

I have the following PDF of a random variable: $f(x)=\begin{cases} 1 & \text{if}\ \ \ 0<x<\frac{1}{2} \vee 1 < x < \frac{3}{2}\\ 0 & \text{otherwise}. \end{cases}$ How can i ...