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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Work out if the relationship between 2 datasets is constant

I have 2 one-dimensional datasets, let's call them a and b. I want to know the correlation between ...
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14 views

Biased MLE estimate of mean (expectation)

Please give an example of p.m.f. or p.d.f. , the maximum likely-hood estimate of whose mean (expectation) is a biased estimator . Thanks
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1answer
22 views

Mean of this experiment

Let the following experience : Let $x=n_0\in\mathbb{N}$. Each step, $x$ has a $1/2$ probability of increasing by one and a $1/2$ probability of decreasing by one. The goal is to ...
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1answer
7 views

Similar to Kruskal-Wallis Test for multidimensional vector

I need to do the similar kind of test as Kruskal-Wallis Test but for the multidimensional vector. Would you please kindly suggest such kind of test or provide some references for N-d case. Thank you ...
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0answers
14 views

solve equation involving digamma function

I have the following equations that I need to solve. $$ \psi(\alpha)-\psi(\alpha+\beta)=X_0 \\ \psi(\beta)-\psi(\alpha+\beta)=Y_0 $$ $X_0$ and $Y_0$ are known constants. Is there a way to atleast ...
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14 views

Inference Two Sample

During the regular season of the NBA, the great Larry Bird made 3,960 free throws out of 4,471 attempts for a career free throw percentage of 88.6%. As of March 21/11, British Columbia’s own Steve ...
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1answer
17 views

Probability with two uniformly distributed cost

I have two uniformly distributed costs that are random and statistically independent. They are 3,000 to 6,000 and 3,000 to 12,000. I am trying to find the probability that the total cost of these two ...
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13 views

Mann-Witney test statistic?

For a Mann-Witney test do we use the T value from the smallest sample size as the test statistic or the smallest T value? I presume it is the former since this is how it is with the wilcoxon rank sum ...
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2answers
19 views

Variance of a dice roll

I am currently working on a problem and am unsure if I approached it correctly. Here it is: ...
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51 views

Is my coin fair — only 11 trials

My task was to flip my penny $11$ times and record the number of successes (heads) and then determine with $99\%$ confidence whether the coin is fair or foul. my $\hat{p}$ is $0.45$, thus $\hat{q}$ ...
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12 views

Business Stats Question Please Help

For students taking online courses at ABC University, grades have been distributed as follows: A – 40%, B – 30%, C – 15%, D – 10% and F – 5%. A sample of 173 students taking online courses at KSU has ...
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2answers
9 views

Determining level of significance when hypothesis is an interval

For a normally distributed sample: σ = 60 Sample size = n = 12 Sample mean = x = 3450 Null Hypothesis = H_o ≠ 3500 Hypothesis = H_1 = 3500 I need to determine the smallest significance level at ...
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1answer
19 views

What can be said about usefulness of two regression lines?

How one can say that the regression equation $y$ on $x$ is more useful than the regression equation $x$ on $y$ as a predicting formula?
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1answer
28 views

Stats Normal distribution [on hold]

A company pays it employees an average wage of $\$15.90$ an hour with standard deviation $\$1.50$ per hour. Assume the wages are approximately normally distributed. a) What proportion of employees ...
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35 views

A city wants to encourage downtown

could you please help me with this ( part d ) A city wants to encourage downtown employees to use public transportation. Below is the time in minutes to get to work on one morning according to ...
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1answer
36 views

Transformation theorem, Cauchy distribution

I have derived the density for the ratio of two independent random variables,via the transformation formula. In this way: $V = X/Y $ and $ U = X $ inversion yields: $Y = U/V$ och $X =U$ , the ...
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42 views

What is this graph called?

I'm not sure what it's called. Update: It's from the NED. Also explain: The name of these 4 axes. I mean I guess Y and X are in the same position but what about the others? The ...
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0answers
11 views

Best system ? Without martingale

I wonder what is the best system, if the percentage of winning bets is 52%. Bets have two options 1 or 2 and is rounded to the average odds 1.80, and the maximum wrong bets  in a  row is 8. So, with ...
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0answers
30 views

How to scale “probabilities” to a given mean?

I have a set of scores $x_i$, $i=1,\ldots,N$ (mimicking probabilities, $0\le x_i\le 1$) and I want to transform them so that the result has a given mean $m$, while remaining in the interval $[0;1]$. ...
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1answer
19 views

BINOMIAL PMF distribution [on hold]

X∼binomial(1,1/3) and Y∼binomial(2,1/2) Obtain PMF of W = XY + 1 How to approach and solve this problem. Can some one help me in this regard? Thanks,
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22 views

PMF FROM BINOMIAL [duplicate]

Obtaining PMF from a binomial distribution (Joint). I have posted my query on this link. Can you please look at it please? thanks.
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0answers
27 views

Can someone help me with the following math question/dilemma?

I have a pool of objects that are randomly selected from a global object database. The objects certain numeric attributes: The objects from the pool are fed to users in real time Users will either ...
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1answer
29 views

How to show that $\Phi(1-x)^{-1} =O(\sqrt{\log{x^{-1}}})$

In the middle of some proof, I have faced an expression $\Phi^{-1}(1-x) =O(\sqrt{\log{x^{-1}}})$, where $\Phi(\cdot)^{-1}$ is a quantile function of the standard normal distribution and $x \in (0,1)$. ...
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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
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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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0answers
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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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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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19 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
10 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
9 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
17 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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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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30 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
25 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 ...
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1answer
38 views

Which voting method is the most fair? [on hold]

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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24 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 ...
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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
38 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 ...
0
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2answers
42 views

Check if a given function is a probability density function [on hold]

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
49 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 ...
2
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1answer
37 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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0answers
17 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 [on hold]

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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22 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
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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 ...