# Tagged Questions

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### Uniform sampling with replacement item frequency

Suppose we are sampling from $N$ distinct items uniformly with replacement $M$ times. What can be said about the distribution of frequencies of items drawn? For example, if I sort all the frequencies ...
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### Computing P-value

In a book, from a sample they derived Mantel-Haenszel chi-square statistic $$\chi_1^2=1.41$$ And it is written that : this $\chi_1^2=1.41$ is associated with a one-sided P-value between $0.10$ and ...
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### generating random samples with a PDF

I have the PDF of a distribution from which it is not possible to get a closed from for the CDF or inverse CDF. Is there a technique that would allow me to generate samples from this distribution ...
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### Non-uniform sampling of N-sphere

Suppose I have a unit $N$-sphere from which I want to draw points at random. To obtain uniformly distributed points I do the usual technique of drawing $N$ random variables $x_i$ from a Gaussian ...
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### Kalman Filter, deriving the conditional distribution for covariance matrix

I have a Kalman Filter model where: 1- State space is $x_{1:N}={(x_1,x_2,...,x_N)}$ and observation space is $y_{1:N}=(y_1,y_2,...,y_N)$ 2-$\mu_1$ and $V_1$ are the mean vector and covariance ...
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### Probability in a Random Sample [closed]

V. The mean monthly rental rate for a two-bedroom apartment in Atlanta is $\$982$(Elle. September 1998). Assume that the population mean is$\mu = \$982$ and the population standard deviation is ...
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### Is it possible to sample the Dirac delta function?

The Dirac delta function can be a probability measure with the unit/Heaviside step function as its cumulative distribution function. Is it possible to sample such a distribution? If a random variable ...
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### An Exercise of noncentral $\chi^2$ distribution.

Let $Y_1,\ldots,Y_n$ be independent random variables with $Y_k$ distributed as $N\sim(a_k,\sigma^2)$, and $\bar Y=\sum_{k=1}^{n}\frac{Y_k}{n}$ denote the sample mean, $S^2$ denotes the sample ...
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### cumulants of non-central $\chi^2$ distribution

Cumulant generating function is defined by logarithm of moment generating function. $$K_X(t)=\log M_X(t)$$ Let $X$ be a non-central $\chi^2$ variate with parameters degrees of freedom, $n$ and ...
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### Convex Hulls in Complex Vector Spaces?

I am trying to generate uniform samples over the convex hull of a set of points that are defined by a set of corresponding vectors with complex entries. In other words, I am trying to generate samples ...
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### Problems sampling from a $pdf$ over $SO\left(3\right)$

I have a probability density function over $SO\left(3\right)$, which I am trying to sample from. The $pdf$ is given as a generalized fourier series:  f\left(\omega,\theta,\phi\right)=\sum ...
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### Sample $x$ from $g(x)$

I got confused with all this randomness and probability functions. I was trying to implement the rejection sampling method which (apparently) is really simple. I was reading from Rejection Sampling in ...
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### please prove the following proof related to F distribution.

Suppose $S_1^2$ and $S_2^2$ are two independent unbiased estimate of the common population variance $\sigma^2$ from two random sample of sizes $n_1$ and $n_2$ respectively. Then show that ...
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### estimate population percentage within an interval, given a small sample

Given a small sample from a normally-distributed population, how do I calculate the confidence that a specified percentage of the population is within some bounds [A,B]? To make it concrete, if I ...
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### How to sample from a Gamma distribution with shape not integer

I'm looking for an effective method to sample from a Gamma distribution that has the shape parameter not integer. However, I found everywhere the method to sample from a Gamma with an integer shape ...
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### generating a binomial distribution

I'm trying to sample from a data set using a binomial distribution with parameters p and n. Implementation-wise, I follow these steps I generate an array containing the values of the cumulative ...
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### How to sample from a product-of-sums distribution?

$A$ is a $M$x$N$ matrix whose entries are positive. $x$ is a $N$ dimensional binary (i.e. consisting of $0$s and $1$s) vector and the number of $1$s in $x$ is constant. Let $y = Ax$. The distribution ...
I have a some questions that have been bothering for a while now. First, how does one obtain the joint probability distribution function of $X_{1},\cdots ,X_{n}$? Would it be \$\prod\limits_{i=1}^n ...