# 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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### 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 ...
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### 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 ...
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### Finding skewness and kurtosis numerically in Mathematica

I have a function given by ...
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### Why does my calculation of a probability take too much time?

I am calculating the value of the following function for given argument values: ...
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### find the conditional probability of winning [closed]

Suppose in a coin-flipping game between two players, A and B. The probability that the coin lands heads up is p(0 ps: the solution can be obtained in the games of m+n but its not the correct ...
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### 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 ...
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...
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Observe: ...
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### 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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### 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): ...
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### 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 ...
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### 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 $var(\epsilon_t)$ ...
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### Find maximum Log likelihood for repeated random variates

I have the following code ...
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### 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 ...
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### 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: ...
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### 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 $\sqrt{x^2+y^2+2xy\cos(\phi)}$, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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 ...