Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory as well as other branches of mathematics such as linear algebra and analysis.

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Calculate the expectation of psi(x) with a gamma density x∼Gamma(α,β )

Suppose I have a Gamma distributed random Variable x∼Gamma(α,β). Now I want to calculate the following expectation values (integrals): E[psi(x)] with psi(x) being the digamma function Many thanks ...
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2answers
14 views

Question on Spearman's Rank Correlation Coefficient

I'm doing some practice questions in my statistics book, and started doing this one: Find Spearman's rank correlation coefficient between X and Y for this set of data: ...
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0answers
13 views

Naive Bayes classfier prove

I have a question about the binary classifier about the way to prove it as a linear classifier. For example, Consider binary classification where the class attribute $y$ takes two values: $0$ or $1$. ...
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21 views

Deal with circular standard deviation

I have a sensor that gives me a direction of the target in degrees with a certain standard deviation and I use a circular probability density function (PDF) to represent probable locations for the ...
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0answers
15 views

Difficult to understand difference between the estimates on E(X) and V(X) and the estimates on variance and std.dev. on lambda-hat

I'm having a very hard time to separate estimates on population values versus estimates on sample values. I'm struggling with this exercise (not homework, self-study for my exam in introductionary ...
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1answer
14 views

Clustering elements according to covariance matrix

I'm doing a little bit of topic modelling (which is not really my area) with twitter tweets. The situation is the following: I have a (sort of) covariance matrix where the entrie $C_{ij}$ corresponds ...
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7 views

Error Bars for percentages [on hold]

Firstly I do appreciate your helps on this issue ! Here is my question : Assume for some different values of X which is our independent variable, we have repeated an experiment N times per each X. We ...
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1answer
15 views

Estimation of standard deviation.

Let $\overline X$ be a mean of any population, $\overline Y$ as well. Now, $ \Theta$ is any unbiased parameter, $X,Y$ are independent. I don't understand a following formula: $\overline \Theta$ is ...
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1answer
18 views

How to use Bayes's rule with mixed distributions?

On page 81 of The Likelihood Principle by Berger and Wolpert (1988) I find the following claim (which references example 20 on page 75). We consider a certain statistical problem from a Bayesian ...
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2answers
18 views

Probability of Independent Events individual vs in series

I understand that independent events (such as a fair coin flip) should not be viewed in succession. For example, if you flip heads 10 times in a row, the odds of flipping the next coin heads is still ...
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1answer
11 views

Understanding a chart about likelihood

I am learning stats from All of Statistics 1e. I understand that likelihood is the probability of a parameter, given some data. So if you flip an unknown coin 1000 times and get 500 heads a parameter ...
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1answer
7 views

Coarse Graining: Correlation destroyed after coarse graining

X Y are two correlated random variable. How likely the correlation between them will be destroyed if the following coarse graining method is applied on them? We divide the range of X and that of Y ...
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11 views

The probability density of samples

I've found many ways to estimate the pdf of the distribution you take samples from. However I did not find any ways to calculate THE probability density of the samples itself. How can I do that? PS. ...
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3answers
30 views

How to understand reproducibility in statistics?

I'm having problems to find info about reproducibility in statistics. The books I have with an starting level in statistics doesn't even mention it. At college, one of my previous professors ...
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1answer
10 views

Function of Jointly Distributed and Convolution

Looking into the continuous case of the sum of jointly distributed RVs in an example in my textbook and there are a few steps missing that I can't seem to wrap my head around. If $X$ and $Y$ are ...
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1answer
22 views

multinomial hypothesis testing

Suppose we have data $(X_1, X_2, X_3)$ (I'll refer the categories as 1, 2, 3) that has a multinomial distribution with parameters $n$ and $(p_1, p_2, p_3)$ and we want to test the hypothesis that ...
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4answers
40 views

Simple coin flip probability

There's are many people saying either one of two answers for this: ...
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0answers
11 views

At which sample size should you approx. a niid variable by z-statistic instead of t-statistic?

I have two datasets with both 50 samples ranging from 1965-2014. (The data contains the returns for W. Buffet over the 50 years and the returns from the S&P500, also over the 50 years.) I ...
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1answer
22 views

Take the outcome of a draw in ELO formula

Is there any way to get the probability of a draw outcome using ELO formula as it only gives the Win probability ELO formula is given by $E = \frac{1}{1+10^\frac{d}{a}}$ where d is the difference in ...
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1answer
11 views

Unbiased estimators for binomial distributed variable

I'm having trouble determining whether the estimator beneath is unbiased or not. First some info: $x_i \sim binom(n_i,p)$ I have a sample of $x_1,x_2,x_3,x_4$ so $n=4$ I want to find out if the ...
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0answers
8 views

Best linear predictor of an AR model

I am how exactly should understand the best linear predictor for an AR(p) model. For instance if we have an AR(1) model defined as $X_t = \phi_1X_t+Z_t$ with $Z_t$ is WN($0$,$\sigma^2$) and I want ...
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0answers
8 views

Statistical Inference in finding Median and Mode [on hold]

What is the Best practice in finding Median and Mode in case of group data,use of class boundary or not? And explain the two practices? Thank you.
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0answers
8 views

Correlation between ordinal variables

I want to know the correlations between 3 groups of variables which are oridinal (rating of 1 to 10). I have followed the formula on wiki and computed the Kendall tau-b correlation coefficients ...
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3answers
41 views

Is it possible to make a dataset given these following mean, range, and standard variance?

Given that the: $Mean = 30$ Range $= X_n - X_1 = 10$ $S^2 = Variance = 40$ is it possible to construct a dataset with those values? So, to be honest I have no idea how to properly approach this ...
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1answer
25 views

How the formula for Pearson correlation coefficient is derived? [on hold]

Recently I have learned using the sample correlation formula to find out the linearity of paired data set (x,y). I was told the properties when the coefficient r is equal to 1/0/-1 but I was never ...
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1answer
21 views

Unpacking the definition of a likelihood function

I am learning stats. My book says let $X_{i}, ..., X_{n}$ be IID with PDF $f(x;\theta)$. It then defines a likelihood function as $$\displaystyle L_{n}(\theta) = \prod_{i=1}^nf(x;\theta)$$ I think ...
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9 views

Problems understanding Autocorrelation/Autokovariance

I am having some trouble understanding the concept of autokovariance/autokorrelation with a timelag l. From how i understand it, it is the kovariance/korellation a series has, with a timelagged ...
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0answers
22 views

At which value is the density in two poisson-processes the same?

Two poisson processes, $X$ with $\lambda=3$ events pr. hour and $Y$ with $\lambda=5$ events pr. hour. Let $Y$ be the waiting time. At what value, $y$, in minutes and seconds, is the density, ...
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0answers
25 views

Gaussian mixture model - mode finding

I'm doing some research, and I stuck at finding mode for gaussian mixture model. I have set of $3D$ points. For each pair of points, I need to calculate following: $\pi_{ij}$ - probability that ...
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0answers
10 views

Gap test for RNGs

Gap test is discussed here gap test for random numbers , if we have probabilities how we can find the expected number of gaps in order to compare with counted number of gaps after running random ...
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1answer
11 views

Completeness - Normal iid sample with the variance known

How to prove that the family of distributions for a normal iid sample with known variance is complete without using the result that this normal family is a member of the exponencial family?
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27 views

Statistical distribution methods

I'm coding a program to classify a stock price movement in a given timeframe. I have around 20k data points and it ranges from 0 to around 300, with the average being 10,8. I want to use a genetic ...
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1answer
28 views

Excpected value of unbiased estimator.

Let $ \Theta$ is any parameter of any statistic such that $\Theta $ has an unbiased, normally distributed estimator $\overline \Theta$. Now, it is written in the book, that: $$E \overline \Theta = ...
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1answer
35 views

Mean and standard derivation

A set of numbers consists of one's and three's. Find the mean and standard derivation if there are 23 one's and 17 three's. What's the meaning of this question ? I know the formula for mean and s.d. ...
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1answer
29 views

Finding the mode of the negative binomial distribution

The negative binomial distribution is as follows: $f_X(k)=\binom{k-1}{n-1}p^n(1-p)^{k-n}.$ To find its mode, we want to find the $k$ with the highest probability. So we want to find $P(X=k-1)\leq ...
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3answers
39 views

What is the relationship betweeen a pdf and cdf?

I am learning stats. On page 20, my book, All of Statistics 1e, defines a CDF as function that maps x to the probability that a random variable, X, is less than x. $F_{x}(x) = P(X\leq x)$ On page ...
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0answers
17 views

Probability with a table

a) P(randomly picking someone going to the concert)= I have .406 but its wrong b) P(randomly picking someone who has kids)= I have .54 but it might be wrong c) P(randomly picking someone who does ...
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1answer
11 views

What does this author mean by “limiting frequency” (in the context of frequentist statistics)

I am reading All of Statistics by Larry Wasserman. On page 176, he says that Bayesan statistics is different than frequentist statistics, in part, because Bayeseans believe that "probability describes ...
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0answers
19 views

Behavior of MGF of Quadratic Combination of Dependent Multivariate Gaussians

Sorry if the formatting is poor, this is my first time asking a question. I'm investigating how squared gaussians behave, using the techniques provided here, which are giving me inconsistent results. ...
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1answer
15 views

Random variables vs sample of mesurement

i would like to know why a sample of measurement in Statistics is being represented through random variables even though it's about only one quality of measurement, say the weight of individuals of a ...
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1answer
13 views

Calculating Margin Of Error

I'm having trouble calculating the margin of error for this problem. "What is the overall margin of error of the survey, at 95% confidence, if it is based on a simple random sample of 1111 voters?" ...
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2answers
33 views

Finding the mode of a distribution

I've been trying to get a better understanding of distributions. So far I understand how we get the formulas for mean and variance (by looking at the derivative of the moment generating function). ...
2
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1answer
32 views

Function with Multiple Periods

Basically I'm trying to fit some data with seasonal effects to a periodic function, and the problem I'm running into is that the local minima usually occur around April, and the local maxima usually ...
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0answers
26 views

Percentage and stats

In Biology class you have $4$ tests, each worth $15\%$ of your final grade, and a final exam worth $40\%$. If your test scores are $80$,$80$,$95$ and $65$; and your final exam score is $85$, what is ...
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13 views

Is the SemiCovariance matrix positive definite?

I am trying to proof whether the SemiCovariance matrix defined in equation (5) from the following paper http://web.iese.edu/jestrada/PDF/Research/Refereed/MSO.pdf is positive definite or not. As a ...
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2answers
21 views

Percentiles and percentage [on hold]

My test grade of $83$ falls in the $74th$ percentile of all grades. About what percentage of students did I score higher than? I thought it was $61.42\%$ but that wasn't right. I thought it was ...
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8 views

hypothesis test type 1 and 2 error

Supporters claim that a new windmill can generate an average of at least 800 kilowatts of power per day. Daily power generation for the windmill is assumed to be normally distributed with a standard ...
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19 views

multivariate interval estimation

I have several samples of probabilistic vectors, i.e, each sample is of the form $(x_1, \cdots, x_n)$ such that $\sum_{i=1}^n x_i\leq 1$ (they are sub-probabilistic vectors), how can I obtain a ...
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17 views

How do i find the percent of packages that will be delivered in less than 16 hours

Couruer service has found that its delivery time is normally distrbuted with a mean of 14 hours and a standard deviation of 3 hours. what percent of packages will be delivered in less than 16 hours?
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14 views

Additive and multiplicative model

I'm new in study of survival analysis. There are some basic-questions that I wanna ask and it will be great if somebody could help me to aswer these following questions: What the differences between ...