# Tagged Questions

1answer
49 views

### 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 ...
2answers
14 views

### How to pick a random sample of given size from a set of unknown size

I have the following problem: I'm reading huge amounts of data records; when done, I would like to display one or more randomly selected records from the data set. It's easy to do if I can cache the ...
0answers
29 views

### How many data points from a sample are in the region $(X>F^{-1}_X (p),Y>F^{-1}_Y (q))$? [closed]

Assume that, there are two variables $X$ and $Y$, and there is is a sample consisting of 1000 observations $(x_i,y_i)$ , $i=1,2,\ldots,1000$, $p$ and $q$ are the quantiles of $X$ and $Y$ respectively. ...
1answer
30 views

### 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 ...
4answers
129 views

### Is it true that $\mathbb E[{\frac{X}{Y}]}={\frac{\mathbb E[X]}{\mathbb E[Y]}}$?

If $X$ and $Y$ are both random variables, does it hold $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
0answers
14 views

### Spherical Sampling of Projected Disk

Given a 2D solid disk centered at some 3D point $\vec{x}$ with radius $r$ and normal $\vec{N}$, I need to compute a random unit vector from the origin that hits the disk. The vector needs to be ...
1answer
45 views

### 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 ...
1answer
21 views

### Sampling on Axis-Aligned Spherical Quad

Given spherical coordinates on a unit sphere, imagine a spherical quad defined by two ranges $[\phi_0,\phi_1]$ and $[\theta_0,\theta_1]$. If you have a globe, for example, the grid formed by the ...
2answers
95 views

### To sample or not to sample?

I have the following issue (I want to predict sports results). Let $X$ be a discrete RV with $m$ possible outcomes, each having probability $p_i$, for $i=1,\ldots,m$. Assume that I have a large iid ...
1answer
68 views

0answers
18 views

### 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 ...
1answer
23 views

### Consequences of violation of independence assumption in ANOVA test

Can you please explain me what is the consequences of violation of independence assumption in ANOVA test? I couldn't visualize it. Does Cochran Theorem relates to ...
1answer
67 views

### How to mathematically prove that we are sampling from same distributions?

The content of this question is about rigorously proving something which is otherwise considered easily correct intuitively. Let's assume we have a multivariate distribution $g(x_1,x_2,...,x_n)$ over ...
1answer
93 views

0answers
30 views

### Relation with $F$ distribution and $t$ distribution

If $X\sim F_{n,n}$ , then show that $$\frac{\sqrt n(\sqrt X-\frac{1}{\sqrt X})}{2}\sim t_n$$
1answer
58 views

### Number of draws needed to get a positive element using a *weighted* sampling without replacement

Imagine we have $M$ elements, where some of them ($y$) are positive and the rest, $z=M-y$, are negative. The probability of drawing any of them is given by a distribution. Let's call $p_1$, $p_2$, ...
1answer
229 views

### probability of a certain event in a repeated sampling with replacement (without ordering)

I have a problem that is bugging me for a couple of weeks now. I have asked some friends etc but the answers were not satisfying at all. So here we go. Suppose we have a set ...
0answers
21 views

### Population size and accuracy of expected value

If I have a series of populations, and a set of outcomes for these populations, how can I be certain that the observed proportions are, in fact, credible? I have investigated certain sampling methods ...
1answer
71 views

### symmetric polynomial inequality?

I put $n\ge 2$ balls of various sizes into an urn. I draw two balls (without replacement) from the urn. With each draw, I draw any given ball with probability proportional to its size. Can you ...
1answer
222 views

0answers
100 views

### 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 ...