# All Questions

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### Does random sampling from a dataset produce the same distribution as the original space?

Let's say we have a dataset $D$ with $N$ rows and $M$ columns. Each column is a feature. And for each feature $X_1, X_2,..., X_N$~ iid $F_p$ where $F_p$ is the distribution for feature p. Now let's ...
41 views

### Population vs Sampling Frame vs Sample

Could someone please explain how the sampling frame is different from population and sample? I understand that the population is all the sampling unit that match our criteria for the study. And the ...
32 views

### Why is the infinite-population perspective usually taken in sampling? What underlying bias/convergence implications are there?

In sampling literature and causal inference literature, there usually is a distinction made about how to view observed data. The first is usually to view some observed data as having come from a ...
43 views

### Prove property of a confidence interval

How does one go about proving the characteristic of a confidence interval that: A 95% confidence interval means if you were to randomly sample the same way 1000 times and create 1000 confidence ...
32 views

### Generate random sample of X1 and X2

If X2 is dependent on X1, how to generate the random sample of (X1,X2)? One scenario is that we know the prior distribution of X1 and functional relationship between X1 and X2, how to generate the ...
18 views

### Why the ratio of (distance from expectation)^2 / expectation in a goodness fit test follow a chi-square distribution?

I know that the sum of square of normal random variables follow a chi-square distribution. But when I learn how to do a goodness-fit test I don't know why the ratio of (O-E)^2/E follows a chi-square. ...
10 views

### Renormalizing a distribution to reduce variance

I have a predictive model $M$ that generates an empirical predictive distribution $P_M$ via a set of samples. I cannot change the predictive model. I can evaluate the predictive performance using ...
28 views

### Does a data-dependent sampling rule induce correlation?

[This question is cross-posted on math SE here ] Suppose I have two iid streams of data that are independent of each other: $X = (X_1, X_2, \ldots)$ and $Y = (Y_1, Y_2, \ldots)$. I want to estimate ...
56 views

### Sampling without replacement - Normal sampling distribution [duplicate]

Most of the introductory stats textbooks, treat the sampling distribution of the mean as a normal distribution when sampling is done without replacement and n/N > 0.1. They just use of the finite ...
148 views

### Why do we use rejection sampling even we know the distribution?

I already read this post and I have the exact same questions. Below I pulled the first question and the answer from the post. Therefore we still use the distribution of p for the randomly ...
2k views

### Difference between “Sampling” and “Subsampling”?

I just got this question in my mind, because I have seen so many times in the literature that these two words are being used alternatively, Sampling and ...
43 views

### Should we identify outliers from population prior to taking sample?

I am revising undergrad statistics course via this course, where i am learning technique to pull out sample from population. While ensuring that sample is decent representative of population, i am ...
30 views

### Expected payoff from a weighted random sampling without replacement?

In an evolutionary game theoretic context, I am interested in calculating expected payoffs of different strategies in a 2x2 game, given a weighted random sampling without replacement from a population....
31 views

### Where do the values for t tables come from?

For a given normal distribution, figuring out what percentage of scores fall between two bounds is straight forward. Calculate the z score and look it up on a z table. Or one can also evaluate the ...
169 views

### minimum number of rolls necessary to determine how many sides a die has

For example, say you have a black box that has a number of n-sided dice in it. You have 4-sided dice, 6-sided, 8, 10, 12, 20 and so on. The die sides are all A except for one side that says B, e.g. ...
4k views

### Why is bootstrapping useful?

If all you are doing is re-sampling from the empirical distribution, why not just study the empirical distribution? For example instead of studying the variability by repeated sampling, why not just ...
90 views

### Maximizing a computationally expensive function

Let $f:[0,1]^{80} \rightarrow [0,1]$ be some function, and say I have a computationally expensive way to calculate $f(x)$ for each $x \in [0,1]^{80}$ (expensive = 40s per query). The goal is to ...
170 views

### Statistics can't be a function of a parameter - but isn't the sample a function of the parameter?

I have a question that relates to this post: Can a statistic depend on a parameter? But on it, the discussion focuses much on the t-statistic given as an example by the question asker. My doubt in a ...
2k views

### What does it mean to sample a data point from or according to a distribution? [duplicate]

I know this is an extremely basic question, but I have never had a course on statistics or applied probability. The only probability I had was in a measure theory course. Now I am doing machine ...
29 views

### Need help with a PMF example

Was reading through my lecture slides and I saw this question I am not sure what or how the prof approached this problem after step 6. It'd be greatly appreciated if anyone can tell me what's going ...
442 views

33 views

### Pandey and Dubey estimator.

I am studying sampling theory Pandey and Dubey(1988) proposed the following product estimator. $\bar y_{PD} = \bar y \left( \frac{\bar x + C_x}{\bar X +C_x}\right)$ And its Mean square error is ...
769 views

### Central Limit Theorem, Skewed Distribution and outlier detection

I'm trying to see how the CLT can help when trying to detect outliers in a distribution. Say I'm pricing houses in a location and that the resulting distribution of my sample of prices is rightly ...
60 views

### Basic question on sampling stream of data

I am reading up an article and came across sampling scenario, but I am not able to come up with intuition behind the numbers presented. Scenario: User issuing search queries to a search engine. "...
361 views

### what is the intuition behind the SRSWOR formula?

I earlier asked about Slovin's Formula (https://math.stackexchange.com/questions/1410492/what-is-the-intuition-behind-slovins-formula), and learned shortly thereafter that it was derived from this ...
556 views

### Mean and variance for unequal samples

I have a sampling of variable sized plots. Each plot contains the number of trees present on the plot. Given: $n=$ the number of plots $s_i=$ the size of the $i^{th}$ plot $y_i=$ the number of trees ...
495 views

### How do I split a normal distributed sample into groups of percentiles but with an additional random noise component for uncertainty?

I have a sample of students that I want to divide into smaller groups based on a their IQ but with a certain random noise component - how can I do that? I need to cluster the best, the average and ...