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.

learn more… | top users | synonyms

0
votes
1answer
16 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 ...
1
vote
2answers
17 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 ...
0
votes
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 ...
0
votes
0answers
5 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 ...
0
votes
0answers
10 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. ...
1
vote
3answers
28 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 ...
1
vote
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 ...
1
vote
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 ...
1
vote
4answers
38 views

Simple coin flip probability

There's are many people saying either one of two answers for this: ...
0
votes
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 ...
0
votes
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 ...
2
votes
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 ...
0
votes
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 ...
-1
votes
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.
0
votes
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 ...
1
vote
3answers
40 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 ...
-3
votes
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 ...
1
vote
1answer
20 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 ...
-1
votes
0answers
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 ...
0
votes
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, ...
1
vote
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 ...
0
votes
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 ...
-1
votes
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?
0
votes
0answers
26 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 ...
-1
votes
1answer
27 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 = ...
0
votes
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. ...
1
vote
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 ...
1
vote
3answers
38 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 ...
1
vote
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 ...
0
votes
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 ...
3
votes
0answers
16 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. ...
1
vote
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 ...
0
votes
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?" ...
0
votes
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
votes
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 ...
0
votes
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 ...
0
votes
0answers
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 ...
-3
votes
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 ...
0
votes
0answers
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 ...
0
votes
0answers
18 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 ...
-1
votes
0answers
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?
0
votes
0answers
13 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 ...
0
votes
1answer
17 views

p value and hypothesis testing

In a random sample of 99 games the home team won 57 games. Test the null hypothesis That home team wins one half of all games against the alternative that the home team wins a majority games. How can ...
0
votes
1answer
30 views

Simultaneous density function of two continuous variables, X and Y.

I'm having issues with calculating the simultaneous density function of two continuous variables, X and Y. I took a screenshot of the information: How should I start? I know that if the two ...
0
votes
0answers
10 views

How to combine 2 different variables (time&cost) into a fitness function?

We are working on a simulation of uber taxi drivers, and to measure the effectiveness of additional functionality (like picking up extra passengers along the way) we would need to create a fitness ...
2
votes
0answers
31 views

Hoeffding’s inequality extension

In Hoeffding’s inequality we assume that the random variables $X_i$ ,$i=1,..,n$ are i.i.d. and bounded . Is there any extension to Hoeffding’s inequality for the case that $X_i$ are identically ...
1
vote
1answer
34 views

Steve Nash’s expected value from his one-and-one free throw situation is 1.72 points. What is his free-throw percentage?

The one-on-one free throw situation works like this - for the first throw, if you make it, you get to do it again. If you miss, you don't get another chance. If you make it the second time, you get ...
0
votes
0answers
15 views

Hypothesis test, p value problem self study

In a random sample ,p=57/99 Hypothesis test H0 : P = 1/2 H1 : P > 1/2 I want to test the H0 and want to find the p value and threshold of significance level. I am trying to solve this problem. I ...
1
vote
3answers
30 views

How to denote an average of data satisfying a given condition

I have to write an expression for the following. I have values, one fpr each of the last 5 months: ...
1
vote
0answers
14 views

bias reduction when the bias depends on the true parameter

Let's say we estimate a parameter, $\theta$, by $\hat{\theta}$. For this estimator we have the following property that $$\hat{\theta}\to_{p}\theta+f(\theta)$$ where $\to_{p}$ denotes convergence in ...