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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Is logistic regression unbiased and efficient?

Seeing how in social sciences the Carmer-Rao lower bound is used as variances of the found parameters it would seem that the parameters are both unbiased and efficient, but what is the proof for this? ...
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0answers
11 views

normal dribution -with mean time and standard deviation [on hold]

The time taken by passengers arriving at an airport has been recorded as follows: The mean walk time from the chocks on of an aircraft that lands to the immigration counter is 5 mts, with a standard ...
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11 views

Creating trendline of one individual over the population data [on hold]

Lets assume I have collected the data about how often people give a coin to beggar depending on the weather outside. So in Y-axis there is donation% from 0% to 100% and X-axis represents how good the ...
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0answers
31 views

In how many ways can you make change for a dollar? [duplicate]

I know there are questions related to this on the site but they are not in the context I am looking for (basic statistics). This problem is at the end of the section introducing combinations and ...
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38 views

Rupam got a question.need help [on hold]

If theta be the angle between two regression line then how i will show that $\sin(\theta)$ less than equals to $1-r^2$? where r is correlation coefficient
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24 views

Bayesian linear regression cost function

I am studying classification using linear regression . Now, I want to map it in Bayesian regression. Let talk about binary classification using linear regression again. Assume that I have a set ...
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0answers
11 views

Number of significant linear predictors if predictors are not independent?

I would like to determine which of a set of candidate predictors $\{x_1, x_2,\ldots, x_n\}$ are significantly relevant to the linear prediction of $y$. Typically, one can compare a full model ...
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0answers
11 views

Threshold calculation

I need to calculate a threshold $[T]$ for a data set. The elements are a total count $[t]$ of items, and of those total items there will be variable counts of hot$[h]$ and Unknown$[U]$. So the ...
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0answers
10 views

Determining Moving-Average Representation of AR(2) Process

Consider a stationary $AR(2)$ process given by $$X_{t} - X_{t-1} + 0.25X_{t-2} = 5 + a_{t}$$ where $a_{t} \sim WN(0,1)$ (white noise). I am interested in obtaining the causal representation of ...
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0answers
23 views

Matlab code for higher order scheme

Can somebody help me how to generate the code for the increment $\Delta$Z in the document I have attached? I know how to generate the rest of the increments but struggling in how to generate ...
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0answers
18 views

Initializing MCMC walkers with ambiguous direction (-/+)

I'm running a sampler program where there are observations given as sample data which are derived from an equal sized population of parameters that are converted to the observations using a known ...
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0answers
31 views

Is it possible to get two different fits, both using a single term Gaussian model?

I am using Matlab to fit Gaussian/normal distributions to image intensities that are binned by 25. I recently used the "hisfit" function and then used cftool > Gaussian > single term (equation is ...
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1answer
26 views

Implications of Standard Deviation > Mean

I have a numerical dataset in which the standard deviation is larger than the mean and I am interested to know what this fact can tell me about the dataset. I have drawn the following conclusions on ...
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0answers
16 views

How to represent the parameters in logistic function

I want to find the parameters in logistic function. I read the guide at here. It very clear to explain. But it did not has final solution that I need. Now, we will consider a basis logistic function ...
0
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1answer
41 views

Which voting method is the most fair? [closed]

I have heard of Plurality Borda Count Instant Runoff Sequential Pairwise voting methods, where it mathematically can be proved which is the most fair and in which situations. From my ...
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0answers
26 views

probability theory books

since I'm going to deepen my knowledge of math stats I was wondering what book I should start from...I need one that covers in the very fine details the following topics trasformations among ...
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0answers
12 views

Sum of a truncated normal random variable and normal random variable (correlated) [duplicate]

I'm wondering if there is a closed form of pdf of sum of a "correlated" normal random variable and a truncated normal random variable. I found a paper providing the pdf for "uncorrelated case" but I ...
1
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1answer
17 views

Model selection in regression: Estimated parameters seem to be “non-significant”

I have conducted an experiment which manipulated three factors (Factor 1: 3 levels, Factor 2: 2 levels, Factor 3: 2 levels). The response variable is binomially distributed (1 = correct or 0 = not ...
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1answer
40 views

Sum of truncated normal random variable and normal random variable

I'm wondering if there is a closed-form pdf of sum of "correlated" normal random variable and truncated normal random variable. I found a paper providing the pdf for "uncorrelated" case, but could ...
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2answers
44 views

Check if a given function is a probability density function [closed]

Given $f(x)=\tfrac1{π(1+x^2)}, ~x\in(-\infty, \infty)$, is it true that $f$ is the probability density function of some continuous random variable?
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1answer
50 views

Fast way to inverse B'CB+D

$\mathbf {A = B'CB}$, where $\mathbf A$ is of dimension $n \times n$, $\mathbf C$ is m by m, positive definite and symmetric, $\mathbf B$ is of dimension $m \times n$, and $n >> m$. Inversion ...
3
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1answer
43 views

Statistical test for “too perfect” random number generator?

I am attempting to characterize some random number generator programs in a very simple way. Specifically, I'm rolling a simulated 6-sided die $3 \times 10^8$ times and keeping a count of how many ...
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1answer
39 views

Can regression to the mean explain the unexpected underperformance (per player-rating) of girls against boys on chess?

I'm somewhat mathematically illiterate, I'd appreciate some help in order to satisfy a curiosity. Concise summary attempt: chess ratings are derived from past performance and therefore thought to be ...
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1answer
25 views

Variance- covariance matrix

Consider $H$ denotes hat matrix and $e$ denotes residual. In the book Applied regression Analysis by Draper/Smith, it is written that : $\mathbb V(e_i)$ is given ...
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1answer
48 views

please help with this one [closed]

am having a hard time to finding the answer to this question especially on the part of standard deviation. a set of 20 observation was found to have a mean of 40 and standard deviation of ...
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0answers
25 views

How to estimate the covariance matrix if the unnormalized pdf is known but integral is intractable?

Assume a $d$-dimensional random vector $x$, whose unnormalized pdf is known as the product of N multivariate t-distribution: $$Pr(x)\propto\prod_{i=1}^nt_{\nu_i,\mu_i,\Sigma_i}(x)$$ Is there any ...
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1answer
13 views

Dummy recoding for more than two categorical variables

Say I am doing a study with 3 different types of fruit and I want to make a regression depending on the type that tries to predict the amount sold. I know that I could make 2 dummy variables: orange ...
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2answers
26 views

Area under Normal Distribution Curve

What is the formula that determines the Z-score table? More specifically, what formula can be used the equate the area underneath the normal distribution curve, without using the table?
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1answer
21 views

Confidence Interval for Regression Coefficient ,$\beta$

In the book 'Applied regression Analysis' by Draper/Smith, it is written that : Obtain individual $100(1-\alpha)\%$ confidence interval for the various parameters separately from the formula ...
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0answers
17 views

what are the joint distribution functions and copula? [closed]

Let $U$ and $V$ be two independent uniform (0,1) random variables and let \begin{eqnarray*} R &=&\sqrt{\frac{U^{2}+V^{2}}{2}},\\ A &=&\frac{U+V}{2}, \\ G &=&\sqrt{UV}, \\ H ...
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1answer
28 views

Optimizing Independent Variables to Maximize Dependent Variable

I looked around online and couldn't find anything that was answering my question so I thought I would take to the stack! I'm interested in knowing if there is a statistical or mathematical way of ...
0
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0answers
11 views

Covariance of independent samples

Let's say that I took a bunch of samples --may be mean age -- from a rural area in Africa and another set of samples from a very different and unrelated population in the US. Moreover, one person ...
0
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1answer
17 views

Is there a way to use the Generalized Mean to find the “best” possible mean to use for a specific data set?

I've recently learned about the Generalized Mean as an abstraction of the many different means, includeing the Geometric, Arithmetic, and Harmonic means, as well as others. It is my understanding ...
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31 views

Change of Variables for two level Guassian model

I have a multivariate Gaussian distribution from which two variables, u and v, are drawn. The next variables, U and V, are U = 1/(u^2+5) + N(0,sig_U) and V = v^3 + N(0,sig_V). U and V are known, ...
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1answer
24 views

Calculating optimum values of $u$ and $m$ from $\mathbb V(\bar {y_2}\prime)=\frac{S_2^2(n-u\rho^2)}{n^2-u^2\rho^2}$

I have to find optimum sample size in sampling on two occasions. Suppose that the samples are of the same size n on both occasions. In selecting the second sample, $m$ of the units in the first ...
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0answers
57 views

Share oranges evenly

There is a boy in a street sharing his oranges with people coming across to him on a street. He has 100 oranges in his basket. The number of people walking toward the boy are unknown and varies in ...
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1answer
44 views

Quite confused about continuous probability distribution

I'm self studying probabilities and statistics, now facing this problem. Use the random variable to represent the exact number of inches yesterday rained. Then the answer showed me a figure ...
1
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1answer
38 views

Finding asymptotes given data

Background: I asked this question on Stack Overflow about how to program in Java or VBA a method to calculate asymptotes given a range of data points. I believe the underlying question would be more ...
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1answer
16 views

Unclear about the definition of payoff in a mathematical statistics context

I highlighted the area of confusion. The author uses payoff without defining it and I'm not sure where this is coming from or what it means. I am not sure why the following is true - "Moreover, if ...
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1answer
22 views

Survival analysis in survey dropouts?

I am working with a survey data set and am curious about who abandoned it before finishing all the questions. I have information on how many questions each respondent answered (no skipping allowed) ...
0
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1answer
29 views

Linear regression as $\dim(\beta) \rightarrow \infty$

Consider the linear regression, $$ Y_i = X_i\beta + U_i \qquad E[X_i'U_i]=0 $$ where $X_i=(1,W_{i},W_{i}^2,..\ldots,W_i^K)$ and $\beta \in \mathbb{R}^{K+1}$. The joint distribution of $(X_i,Y_i)$ is ...
1
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1answer
14 views

Should we convert a grouped distribution to continuous if we have to find the median?

Today, in a math exam, I had to solve this question: In the following distribution, write the upper limit of the median class: $$\begin{array}{|c|c|}\hline ...
1
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1answer
17 views

Can't understand the parameters in adjusted R squared

I suppose this is a really stupid question, so please excuse me, but I can't get it. I'm using Simple Linear Regression (Least Squares) to find a line, fitting some points. The points are actually ...
2
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2answers
57 views

Probability of Getting a “Perfect Score” in the Card Matching Game Concentration

A person is playing the card matching game concentration. There are 40 cards, 20 pairs total. All the cards are shuffled and placed at random face down. A turn consists of two moves and a move is ...
2
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2answers
33 views

Dice Rolling 4d10 with a twist

Suppose I roll two 10-sided dice, 1 die has numbers o, 10, 20, 30 etc to 90. The second die has numbers 0, 1 ,2 etc to 9. These dice are used to create a number from 1 to 100 - example: the first ...
-4
votes
1answer
80 views

Prove that if $X \sim N(\mu, \sigma^2)$, then $X \sim \mu + \sigma N(0, 1)$ [closed]

As above. Also how is the general case proved for multivariate Gaussian? edit: I'm not sure why people voted to put this on-hold, it's just asking for a justification of a commonly used statistical ...
3
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1answer
23 views

Should I use odds ratio or risk ratio?

I am doing a retrospective cohort study with sample size 600 and disease prevalence rate greater than 10%. I am leaning more towards using risk ratio because it is easier to interpret and because ...
2
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2answers
15 views

Second moment of chi squared distribution

I've got difficulties in computing the second momentum of chi squared. Chi squared distribution with $n$ degrees of freedom is the sum of $n$ independent distributions $X^2$, where $X \sim N(0;1)$. ...
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0answers
27 views

Probability problem (reliability) [closed]

Assume that there are 30 cells per string. The designer is using metallic interconnects welded to the solar cells and reverse-voltage-blocking diodes connected to the ends of the cell strings by ...
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3answers
61 views

Conceptually: A set whose elements can only be probabilistically characterized?

Sorry for the informality here, but was musing over the basic concepts around describing a set in real world usage: A finite set of explicitly named elements, this apple and that apple, nothing more ...