# 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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152 views

### Can this probability function speed be improved?

I have a process that as part of it requires a certain probability query, specifically, given a multinomial distribution with f equiprobable categories and r trials, some specific category has a given ...
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### Confidence interval

With data = {{0.002, 2.51053}, {0.004, 2.54217}, {0.006, 2.55543}, {0.008, 2.54247}}; I obtain a linear fit 2.51038 + 5.454 x; ...
456 views

### Multivariate linear regression

Say I have a 4-dimensional data set with two independent variables x1, x2, and two dependent variables y1, y2, i.e. each row is <...
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### Why doesn't this function TransformedDistribution work?

According to the information in this post, we know that $z={\sqrt {-2\ln U_{1}}}\cos(2\pi U_{2})$ follows a normal distribution, and the datas generated supports this view. ...
166 views

### How to use MMA to simulate the German tank problem

In the statistical theory of estimation, the German tank problem consists of estimating the maximum of a discrete uniform distribution from sampling without replacement. In simple terms, suppose there ...
90 views

### How to find the expectation $\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right]$?

I'm trying to find the following expectation $$\mathbb{E}\left[ a \mathcal{Q} \left( \sqrt{b } \gamma \right) \right],$$ where $a$ and $b$ are constant values, $\mathcal{Q}$ is the Gaussian Q-function,...
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### How to compute summary statistics and quantiles of user defined discrete distribution? [closed]

I am interested to find out the mean, median, Variance, Skewness, Kurtosis and Quantiles of the following discrete distribution with pmf (E^((1 - E^[Nu]) n) [Nu]^x BellB[n, x])/x! with x=0,1,2...... ...
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### Computing expected value of multinomial variables

We consider a two-dimensional dicrete probability distribution on $\mathcal{X} \times \mathcal{Y}$ with $|\mathcal{X}|\cdot |\mathcal{Y}| = r \cdot q$ distinct values with corresponding probabilities \$...
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### Smooth Kernel Distribution

I have 20060 dates and I used the SmoothkernelDistribution function to get a distribution of them: However, I also need a functional form of the distribution to use it in another program without use ...
53 views

### How to get a list of exponentially distributed points sampled in a range

I want to get 256 points exponentially sampled in a range, and then get its histogram. If I plot PDF, I get the following: ...
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### FindDistribution[] with error bars? (And a ChiSquared Question)

I've got some data defined as follows: ...
867 views

### How to solve the Monty Hall problem?

Problem For purely recreational purposes I would like to solve the Monty Hall problem with Mathematica using the function Probability (dedicated to the calculation ...
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### How to calculate and plot the joint distribution probability density function of independent variables

Knowing that X and Y are independent of each other and follow the standard normal distribution, I want to know how to find and ...
105 views

### Expectation of product of independent random variables (using Expectation function)

I'm trying with no luck to get Expectation to calculate the expectation of expressions containing sums of products of independent random variables. For instance, ...
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### How to use Quartiles to work the same as TI-83 calculator? [closed]

The statistics book I am using defines quartiles the same as Method 1 explained in wikipedia. Use the median to divide the ordered data set into two-halves. If there is an odd number of data points ...
135 views

### Calculate combined standard deviation

If I have a data that I fit with NonlinearModelfit that fits a data based on two fitting parameters, c1 and ...
42 views

### How to calculate with right probabilities values?

My code solves the equation G(Ht) using random p probabilities for each value of d in my <...
48 views

### Confidence interval considering the division of 2 means with different CIs? Statistics

I have the mean and its confidence interval (standard deviation and size of its sample) of 2 different data A and B. I want to divide A/B and get the confidence interval of its division. Is there a ...
46 views

### Using NIntegrate to reproduce NProbability over joint Gaussian distribution

Consider a random vector {s,c} with a bivariate normal distribution. For a vector of positive scalars {a, ß, σz}, I'm interested ...
59 views

### Contribution of 3 groups of data to an overall PDF

I have a time series that is comprised of 3 subgroups. I want to know how I can calculate the contribution of each of these subgroups to the overall PDF. ...