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2
votes
1answer
21 views

How can I uniformly draw points from an ellipsoid?

Specifically, given a positive definite matrix $A \in \mathbb{R}^{n \times n}$, how can I efficiently generate points $x \in \mathbb{R}^n$ that satisfy $x^TAx \leq 1$? I know how to do this when the ...
0
votes
0answers
18 views

Statistics, measuring unknown mean with standard deviation and probability

So I am stuck on this question and wondering if anyone can give me any hints towards it Estimate the mean pH of rainfalls in an area. Previous studies showed that the standard deviation in the area ...
0
votes
3answers
42 views

Sampling Distribution; Statistics. Please verify my answer

Professor earns average $ \text{\$} 65,500$ per year with standard deviation of $\text{\$}3,500$. Random sample of $64$. a. Describe sampling distribution of sample mean $\bar{x}$ of average ...
1
vote
0answers
20 views

Sampling Distribution of the Mean

I want to know if my reasoning is correct. Let's say I got two normal distributed variables: Variable "X": 5.4 (mean), 2.856 (variance) Variable "Y": 5.4 (mean), 5.062 (variance) Let's pick 16 ...
0
votes
1answer
27 views

Bivariate sampling for distribution expressed in Sklar's copula theorem?

In the univariate case, one can easily sample a distribution via random numbers $u\sim[0,1]$ and plugging into $F^{-1}(u)$. I have a bivariate distribution constructed via Sklar's theorem on Copulas: ...
1
vote
0answers
16 views

recovering bits from distorted signal

I have a signal: $r(t) = \sum_k a_k g( lT/2 -k(T+\Delta T) )$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi t/T}$, $T/2$ is the sampling period, and $\Delta T$ is a ...
0
votes
0answers
15 views

Sampling combinations (from a binomial coefficient) without replacement

The total number of combinations of $k$ items out of $n$ total is $n \choose k$, or a binomial coefficient. This can be a very large number even for pretty small $n$. The binomial coefficient ...
0
votes
0answers
16 views

Oversampling and trees

I want to create a model to predict the propensity to buy a certain product. As my proportion of 1's is very low, I decided to apply oversampling (to get a 10% of 1's and a 90% of 0's). Now, I want to ...
0
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0answers
3 views

Sampling subsets to fit item probabilities

I have a set of $n$ items. Each item has a target probability $p_i$ so that $\sum_i p_i = k$. I want to sample subsets of size $k$ of the $n$ items so that for every $i$, the probability that $i$ is ...
-1
votes
0answers
17 views

Understanding Linear Regression

Hello all. It's really good to be in here and I appreciate greatly to all the gurus who help people with their knowledge. It would be really nice if someone could help me out and suggest me with ...
1
vote
2answers
117 views

Probability of a normal random variable added to a number being greater than another normal random variable, and distribution of average

$X$= random height of a male $Y$= random height of a female $X$ and $Y$ are independent of each other For $x$, $\mu=180\text{ cm}$ and $\sigma^2= 16\text{ cm}^2$ For $y$, $\mu=170\text{ cm}$ and ...
0
votes
0answers
8 views

Reconstructing symbols from another set of symbols

I have a discrete-time signal as: $r_l = r(lT/2) = \sum_m h_m \alpha_{l-m}$ where $\alpha_l = \sum_k a_k g(lT/2 -k(T+\Delta T))$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {\sin(2\pi t/T)}{2\pi ...
0
votes
0answers
6 views

Sensitivity analysis of paramaters and input variables

I am trying to perform a sensitivity analysis of an optimization problem $f(x,\alpha)= \min_{ Q} {g(x,\alpha , Q)}$ where $x$ is an input variable for our function, and $\alpha $ is a parameter. ...
1
vote
1answer
50 views

Expected number of distinct nodes visited in a directed bipartite graph

Let $G = (V,E)$ be a directed bipartite graph with $V = \{I \cup O\}$ where $\left\vert{I}\right\vert = n$ and $\left\vert{O}\right\vert = m$. All the edges start from a vertex in $I$ and end on a ...
0
votes
0answers
4 views

Expected number of distinct nodes visited in a directed bipartite graph

Let $G = (V,E)$ be a directed bipartite graph with $V = \{I \cup O\}$ where $\left\vert{I}\right\vert = n$ and $\left\vert{O}\right\vert = m$. All the edges start from a vertex in $I$ and end on a ...
0
votes
0answers
14 views

Sampling Question about Sample Size

A random sample of $16$ has a sample mean of $400$ and a sample standard deviation of $15kg$. Assume normality. A $90\%$ confidence interval for the mean is? I got $(393.43,$ $406.57)$. ...
0
votes
0answers
17 views

Outcome of multiple samples on continuous probablity function

I'm timing a signal from it's generation to return, and trying to figure out the error due to the difference between when the signal is actually sent out / received and when the clock starts/stops, ...
0
votes
0answers
18 views

Sampling from a random distribution with a margin of error

A survey of a population is taken using sampling. It is determined that 70% prefer option A and 30% prefer option B with a margin of error being 5%. Typically when simulating the process with the ...
2
votes
0answers
21 views

Reconstructing a signal at twice the bit-rate

I have a discrete-time signal as: $\alpha_l = \sum_k a_k g(lT/2 -k(T+\Delta T))$ where $a_k \in \lbrace\pm 1\rbrace$, $g(t)=\frac {sin(2\pi t/T)}{2\pi t/T}$, $T$ is the bit period, and $\Delta T$ is ...
0
votes
1answer
33 views

Distinguishing between two weighted dice (or discrete distributions)

In a bag, there are two dice, each with sides weighted differently. I know the weighting of the two dice. I reach into the bag and pick one out with equal probability. I want to know how many rolls it ...
0
votes
0answers
23 views

Box Muller Transform - Proving that Z is Normal Distribution

I'm studying the Box Muller transform and I cannot see how Z0 and Z1 represent standard normal distributions. I've looked at the wikipedia page for the box-muller function but they don't seem to have ...
2
votes
1answer
39 views

Fast fourier transform and nyquist frequency

Trying to figure out how to use Matlab to calculate the nyquist frequency of a signal. Given a function, lets say $y = 5\sin (2t + \pi /3) + \sin (t + \pi /2)$ for $t > 0$. How do we use a fft in ...
2
votes
1answer
16 views

Can I use one float random number to generate two random numbers, one discrete, one continuous?

I need two random numbers. The first one, u, is discrete and takes 70% of the time the value 0 and 30% of the time the value 1. The second one, v, is continuous and takes values uniformly inside [0, ...
0
votes
0answers
4 views

Difference between variance of an IID sampling distribution and the variance any sampling distribution?

If I have a population {1,2,4,4,9} and a sample size 2, the possible samples are: {1 2}, {1 4}, {1 4}, {1 9}, {2 4}, {2 4}, {2 9}, {4 4}, {4 9}, {4 9}. I understand that the mean of the sampling ...
0
votes
0answers
13 views

Find function of error in sampling

I was given a teaser that I can only figure out half of. Imagine there is a dartboard that is centered at (0,0). Darts are thrown and the coordinates are modeled ...
1
vote
0answers
9 views

Number of samples with replacement to reach expected coverage of population under non-uniform sampling

I am interested in finding the number of times $n$ I need to draw with replacement from a population of size $N$ such that the expected proportion of the population seen is at least $P$. From this ...
0
votes
1answer
26 views

Paths of Nearest Neighbours

I'm working on a project about sampling points, where the next point to be added to sample is the closest point to the current point. Furthermore, each point can only appear once in the sample. ...
0
votes
0answers
4 views

Compute mean of a set from a biased sample

I want to compute the average of an unknown set $S$ containing real numbers. I can take arbitrary large number of samples from $S$, but the samples are not uniform, meaning that some numbers are ...
0
votes
1answer
24 views

antithetic sampling

I am reading a book on antithetic sampling.It is said that the idea of antithetic sampling can be applied when it is possible to find transformation of $X$ that leave its measure unchanged (for ...
0
votes
0answers
7 views

Sample from a distribution using the log of the pdf?

I am reading about slice sampling and I understood (that as Gibbs sampling and other algorithms) you can use it when you do not know the exact pdf of the distribution, but rather a proportional ...
1
vote
1answer
33 views

Sin wave, sampling and plotting (Python)

I am not sure if this is the right forum for asking this question, or was it the stackoverflow, but anyway I'll go with it. So I have this python code (in a python notebook, with inlined pylab): ...
0
votes
1answer
16 views

Interpreting confidence interval of regression coefficient.

In a Simple Linear Regression analysis, independent variable is weekly income and dependent variable is weekly consumption expenditure. Here $95$% confidence interval of regression coefficient, ...
0
votes
2answers
43 views

Population estimate from sample

This seems very basic but I can't find a clear statement of it. Suppose I have a population of N balls which are red, white, and blue in some proportion. If I take a sample of S balls (S << N) ...
0
votes
0answers
7 views

Calculating average with special summary statistics

We want to compute the mean of a data set D. The data set is not accessible. Instead we repeatedly gain access to average and size of a subset of D, which contains a data point d $\in$ D and some ...
0
votes
0answers
3 views

Motivation for definitions of Frame, Sampling Set

In a Hilbert Space $\mathcal H$, a frame $\mathcal F=\left\{ f_n \right\}$ is a sequence of vectors that satisfy $$\forall f\in \mathcal H : A\|f\|^2\leq \sum_n | \langle f,f_i \rangle |^2 \leq B\| ...
2
votes
0answers
26 views

Stratified Sampling: Total and mean estimate of population

Question: In a sample survey designed to estimate the total number of cattle, the universe of 2072 farms was stratified into 5 strata on the basis of the total acreage of farms. In the hth stratum (h ...
0
votes
0answers
27 views

Is there a two-dimensional method to optimally allocate N sampling points on a continuous function with derivatives?

I am looking for a method to optimally allocate sampling points. I have read some papers on this topic that discuss one-dimensional allocation using chebyshev points, but I haven't found a good ...
-1
votes
2answers
27 views

Does the sampling distribution coincide with the population distribution if every possible sample is taken?

Say you have a population. You take random samples repeatedly, and the distribution of all the means of those random samples is the sampling distribution. Right? So does that mean, that if you take ...
0
votes
0answers
19 views

Largest hole in uniform sampling of $m$-torus

Let $M$ be the flat m-dimensional torus $(\mathbb R/\mathbb Z)^m$ with the standard Riemannian metric. I would like to know the probability that, given a uniform sampling $X$ of size $N$, there is a ...
0
votes
2answers
40 views

Difficult Survey Sampling question

Question: A Secretary of State wants to survey the primary owners of motorcycles registered in the state to estimate the proportion who want the license plates redesigned. (Primary owner means that ...
0
votes
1answer
35 views

The distribution of sample proportion for given population proportion and sample size

If the population proportion is 0.90 and a sample of size 64 is taken, what is the probability that the sample proportion is more than 0.89? (4dp) work: $n=64$, $\hat p=0.89$, so $X=n \hat p ...
0
votes
1answer
16 views

Random sampling, need some help and guides

i was asked to do an assignment on examining the Body Mass index of students. I have to select at least 50 students from my school, and i was asked to describe how I ensure the randomness of the ...
0
votes
0answers
51 views

simple random sampling without replacement proof

For simple random sampling without replacement, starting with the expectation of $\sum_1^n(y_i-\bar Y)^2$, show that $V(\bar y)= (1 − f )S^2/n$ this looks very hard i tried to simplify the right ...
0
votes
0answers
15 views

Ergodic Versus non-Ergodic Processes

Besides time averaging not carrying over to the ensemble average (in the limit), what are the pros and cons of ergodic and non-ergodic processes? Suppose you were in an engineering situation and you ...
0
votes
1answer
50 views

Examining the effect of a quantitative factor on response.

To examine the effect of a quantitative factor temperature on yield,the researcher has a plan to use the following model for the analysis: $$y_{ix}=\beta_0+\beta_1 x+\epsilon_{ix}$$ where $y_{ix}$ ...
0
votes
0answers
53 views

How does accuracy of a survey depend on sample size and population size?

Which survey is more accurate? Assume the samples are taken perfectly randomly. A sample of 100 people out of a population of 1000 (sample is 10% of population) A sample of 1000 people out of a ...
1
vote
1answer
18 views

reconstruction through sinc interpolation

I have a discrete-time signal $x_k = \sum_l a_l g(kT - l(T+\Delta T))$ where $g(t) = \frac {\sin(\pi t/(T+\Delta T))}{\pi t/(T+\Delta T)}$. Since the signal $x$ has been sampled at rate $1/T>2 ...
0
votes
1answer
22 views

sample and population (set or collection)

In my Statistics class they introduced a population as the set of all measurements of interest to the investigator(e.g. height of humans) and a sample as a subset of the measurements selected from the ...
0
votes
0answers
21 views

Confidence interval of a poisson variable $\hat \lambda$ while using importance sampling to estimate $\hat \lambda$

I want to estimate $\hat \lambda$ by taking $n$ samples from a population $k$. I will sample $n$ items from population $N$ with a sample distribution $P(X)$. Therefore, my best estimate is $\hat ...
3
votes
1answer
25 views

Determine sample size according to some unknown distribution with given error rate and confidence

Assume $x\in\mathbb{N}$ obey some unknown distribution, and I can sequentially and independently acquire infinite samples of $x$. Now, given an error rate $\epsilon$ and confidence $1-\delta$, can I ...