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Questions tagged [probability-or-statistics]

Questions about systematic data collection and organization, or the application of probability theory to model the inherent patterns and properties of sampled data, underlying data distribution(s) or random processes.

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Prove that of two discrete random variables X and Y are independent [on hold]

Prove that of two discrete random variables X and Y are independent, then H(X|Y) = H(X).
35 views

How can we calculate the probability for different events [on hold]

For example, You send out three messages for help: a smoke signal that has probability 0.1 of being seen a message in a bottle that has probability 0.2 of being found a carrier pigeon that has ...
23 views

Compute entropy of the following random variables

Compute entropy of the following random variables: the random variable X that takes the values 0, 1, with probability 1/2.
66 views

Set Theory Question [on hold]

Q: Sum 40 balls in a box, 8= Blue, 13= Black, remaining= grey, I pick 5 balls randomly, pick another then put 1 back, pick another then put 1 back, i. Then return a ball & pick another ...
30 views

Expression with Boole

Let us have an expression for example, this: 2 (-1 + p) (3 - 4 p + 2 p^2) Boole[\[FormalX] == 1] - 9 (1 - 2 p + p^2) Boole[\[FormalX] == 2] ... For the whole ...
34 views

One Function of Two Random Variable

I wonder how to implement below derivation in wolfram mathematica. I want to see integrate results like below picture. Can you help. I used "TransformedDistribution" but it shows only distribution ...
27 views

Are these TransformedDistributions identical?

If A1 and A2 are independent random variables, and B1 and B2 are as well, then are the following TransformedDistributions the same? ...
1k views

How to implement Kullback-Leibler divergence using Mathematica's probability and distribution functions?

Last year Jens answered a question about how to implement Kullback-Leibler divergence in the discrete case. He gave this answer: ...
27 views

Need help with plotting a probability distribution

I looked through the Mathematica directory and could not find a solution that is right for me. I already solved the mathematics behind this problem, I just need to visualize it in a plot. I am ...
448 views

A summary command for statistics

In R I can do: summary(data) Which gives the min, max, median, first, and third quartiles. Is there a similar single command in Mathematica for this? I know I ...
76 views

Speeding up Probability using Monte Carlo

I have a recipe for generating custom distributions, which I want to use Probability[...] on, but am finding that with more than a few variables it very quickly becomes intractable (it runs for hours)....
1k views

How to fit a linear model in the Bayesian way in Mathematica?

Basically, I'm looking for the Bayesian equivalent of LinearModelFit. As of the moment of writing, Mathematica has no real (documented) built-in functionality for ...
53 views

RandomVariate drawn from a custom distribution function takes forever to finish

I'm using the following custom-defined PDF: ...
64 views

1k views

Does Mathematica have an implementation of the Poisson binomial distribution?

I need to work out the probability of having $k$ successful trials out of a total of $n$ when success probabilities are heterogeneous. This calculation relates to the Poisson Binomial Distribution. ...
447 views

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710 views

Integration of linked PDFs over probability simplex

I'm trying to integrate the following expression: f[a1,p1+p2+p3+p4]*f[a2,p2+p3+p4]*f[a3,p3+p4]*f[a4,p4] Where ...
218 views

conditional probability of dependent random variables

Suppose I have 3 random variables: $$X \sim \mbox{Bernoulli}(1/2)$$ $$Z \sim \mbox{Normal}(0,1)$$ $$Y = X+Z$$ How do I compute the conditional probability density: $$P(X=1 | Y=y)$$ Attempt1: <...
77 views

Idiomatic way to obtain conditional density function from a continuous joint distribution

Context In Mathematica one is able to directly calculate the marginal and conditional probability distributions of a discrete joint distribution (abstracting over the specific details) like so: ...
62 views

TransformedDistribution

I am trying to perform some calculations on a random variable that is the sum of a normal distribution and a truncated normal distribution. My understanding is that using ...
139 views

Assign Error bars for y-intercept

I have some data (x,y) with error bars in y direction: ...
131 views

Structural Breaks in a Time Series Model

The Chow test is a test of whether the true coefficients in two linear regressions on different data sets are equal. In econometrics, Chow test is most commonly used in time series analysis to test ...
79 views

Obtain reduced chi-squared for fit

Dear Colleagues, I have performed a fit according to the code below. The last step is to obtain the value for the reduced chi-squared for the goodness of fit. Does mathematica have a ...
113 views

Symbolic integration of logmultinormal distribution

I have been trying to integrate and compute moments of LogMultinormalDistributionin Mathematica, but the integrals don't seem to evaluate. Say for the first moment, ...
348 views

Why is my read in of data taking so long?

I'm just trying to read in some data before I do some calculations. The data set is over 200,000 values that look like this: Here is the code I am using: ...
86 views

Compute the potential of confusion between two matrices

I have a problem. Any help will be appreciated. In order to calculate the accuracy, sensitivity, sensibility and F1 score between diseases and their symptoms, I have two matrices with a different ...
86 views

TransformedDistribution doesn't seems to work properly in this case

Im trying to get the distribution of the random variable defined by $$Y_n:=\left|\sum_{k=1}^n e^{ i X_k}\right|$$ for arbitrary $n$, where $X_k\sim U[0,2\pi]$ i.i.d. Then I had written the code <...
3k views

How to set up a simple Monte Carlo simulation?

there is a 1% chance that there will be a scattering event, if there is a scattering event the direction of scattering will be determined by a random sample of the custom[a_] function and if there is ...
674 views

Is there a package for Bayesian Linear Regression?

Is there a Mathematica package for Bayesian linear regression? Thanks
42 views

Best Way For Estimating Parameters Of Hidden Markov Process

Parameter estimation is not stable. First, make a model. ...
97 views

How can I calculate the expected value of the sum of “n” i.i.d. variables with any distribution?

Particulary, I would like to find the expected value of the sum of $n$ variables distributed like ParetoDistribution[1,1.14]. For example, this works for the sum of two vars with Gamma distribution: <...
How to find the shape parameters of of a beta distribution given the position of two quantiles? I am trying to find $\alpha$ and $\beta$ the shape parameters of a beta distribution. I know that my ...