# Questions tagged [sampling]

Questions about the statistical process of sampling from a population, in order to obtain information for use in statistical learning, estimation, hypothesis testing about some population or process. Use this tag along with the tags (probability), (probability-theory) or (statistics).

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### Best way to estimate probability of heads of a biased coin

What is the best way of estimating the probability p of getting heads in a biased coin? An intuitive idea is to flip it over an over again, and look at the empirical frequency etc, MLE type ...
25 views

### categorical sampling

I want to understand the proportions of different calling type managed by a customer services. I don't know the type of categories (es: payments, product, services, etc...) and the proportions (es: ...
10 views

### Expectation using samples from a population

There is a population $\mathrm{X} = \{x_1, \ldots, x_N\}$ and a function $F(X) = \sum_{i=1}^N f(x_i)$. A subset $S$ of $\mathrm{X}$ such that $|S| \le N$ is sampled using simple random sampling ...
39 views

### Monte Carlo computation of probability of a subset of samples

I would like to compute the probability for some subset $\omega \subset \Omega$ of events to occur, i.e. $P(\omega) = \sum_{x \in \omega} P(x)$ where I know $P(x)$ for all $x \in \Omega$, which are ...
31 views

### Naive Monte Carlo Sampling vs. Importance Sampling

Can someone help me understand this paragraph: The naive Monte Carlo estimator introduced in the last section performs well if the prior and posterior distribution have a similar shape and strong ...
24 views

### How to compute minimum sample size of a simple linear regression model with given statistics values

Suppose the statistics values are given as follows: $\sum_{i=1}^{n}x_i, \sum_{i=1}^{n}y_i, \sum_{i=1}^{n}x_iy_i, \sum_{i=1}^{n}x_i^2,\sum_{i=1}^{n}y_i^2$ Firstly, we can compute the regression ...
14 views

### Combining non-independent random normal-distributed variables

In the below question part b) involves combining normally-distributed random variables which ARE independent. Part d) involves combining normally-distributed random variables which are NOT independent....
35 views

### Statistical estimator of expected value of the gradient of an unknown function

Fix a probability space $(\Omega, \mathcal{A}, \Bbb P),$ a continuously differentiable function $f:\Bbb R^n \rightarrow \Bbb R,$ and a random vector $X: \Omega \rightarrow \Bbb R^n.$ Furthermore, we ...
16 views

### Random sample from Normal Distribution, why isn't the variance divided by n?

Below is a question containing parts b) and c). Further below is the mark scheme. In part c) they take a random sample from T, which is normally distributed. I was expecting the distribution to change,...
1 vote
23 views

### Maximizing the ratio of expected maximum of n IID and the expected value of the IID for a (WHP) non-negative distribution

I’m looking for a distribution that is non negative , or has good tail bounds (so non negative with high probability) and maximizes the following property: $X_1, X_2, …, X_n$ are n IID samples of the ...
42 views

### Do individual Metropolis-Hastings map preserve the target measure?

Consider the probability space $(Q,\mathcal{B}(Q),\pi)$, where $Q \subseteq \mathbb{R}$ is a sample space, $\mathcal{B}(Q)$ is the Borel $\sigma$-algebra on $Q$, and $\pi$ is some probability measure ...
18 views

### the mean and standard deviation aren't the same as those of the input data i provided after sampling

have a log-normal mean and a standard deviation. after i converted them to the underlying normal distribution's parameters mu and sigma, I sampled from the log-normal distribution however when i take ...
25 views

### Central Limit Theorem "find sample size" question, with modulus inequality

I'm doing the below Central Limit Theorem question. I omitted sub-question a) and b) as they were unrelated. I have included the answer below the question. I half-understand the answer but I don't ...
16 views

### Covariance between two sample means sampled successively without replacement.

Lets say i have a population of size N, where N > 1, with the values $y_{1},y_{2},y_{3},y_{4}, ... , y_{N}$. (Unknown Population Distribution) Step 1: A Simple Random Sample without Replacement is ...
12 views

### Generating samples from the joint distribution

If I have samples from two correlated random variables $X$ and $Y$, would it be possible to simulate samples from their joint distribution?
32 views

### Rigorous proof of the Box-Muller transform method

The Box–Muller transform can be described as follows: Let $U_1$ and $U_2$ be independent uniformly distributed random variables on $(0,1)$ and \begin{align}R&:=\sqrt{-2\ln U_1};\\\Theta:=2\pi U_2.\...
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