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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Combination Problem with Sofa

Suppose we have 5 sofa in which 4 persons seated on these sofa on main room. the persons go to another room for eating dinner and after that come back to main room. how many way the persons can seat ...
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interpretation of gross reproduction rate and net reproduction rate

If GRR=1.234 then what can be said about the population growth? And then what can be said when net reproduction rate, NRR=1.234?
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18 views

Sufficient statistic

Let $\mathbf{X}=(X_1,\ldots,X_n)$ with joint frequency function $f(\mathbf{x};\theta_1,\theta_2)$ where $\theta_1,\theta_2$ vary independently. The set ...
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19 views

How to compute the difference between two numbers using a weighted formula?

Currently at work we use the formula ((expected-actual)/expected)*100 to show the difference between two numbers, however, this formula shows extreme differences for small numbers. For example, in the ...
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12 views

Covariance in error propagation

Given the formula: $$ \sigma_{y_0}^2 = \left(\frac{\partial y(x_0)}{\partial a}\right)^2\sigma_a^2 + \left(\frac{\partial y(x_0)}{\partial b}\right)^2\sigma_b^2 + 2 \frac{\partial y(x_0)}{\partial ...
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33 views

In 30 boxes are 15 balls. Chance all balls in 10 or less boxes?

Question1: I found 30 boxes. In 10 boxes i found 15 balls. In 20 boxes i found 0 balls. Afer i collected all 15 balls i put them randomly inside the boxes. How much is the chance that all balls are ...
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22 views

Adding statistical weight to reviews

I'm trying to prioritize a list of places using a few factors: Number of reviews for each place Percent of people that recommend each place (from the pool of people that reviewed) Overall rating of ...
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1answer
18 views

Total boundness of Lipschitz densities

In the article Almost Sure Testability of Classes of Densities by Devroye and Lugosi in 1999. They claim in Example 10 (page 9) that Lipschitz densities on [0,1] with Lipschitz constant bounded by ...
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1answer
55 views

Explain why $\big(\int_{-\infty}^{\infty}e^{-z^2/2}dz \big)^2 = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(z^2 + u^2)/2}dzdu$

I came across the following when studying a proof related to the normal distribution: $$\left(\int_{-\infty}^{\infty}e^{-z^2/2}\ dz \right)^2 = \int_{-\infty}^{\infty}\int_{-\infty}^{\infty}e^{-(z^2 ...
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33 views

$\overline{\theta}$ the maximum likelihood estimator of $\theta \implies$?

I can't understand how the following statement holds without any extra conditions on the function $g$: $\overline{\lambda}$ the maximum likelihood estimator of parameter $\lambda \implies ...
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65 views

Expected area of a random triangle with fixed perimeter

I'm trying to calculate the expected area of a random triangle with a fixed perimeter of 1. My initial plan was to create an ellipse where one point on the ellipse is moved around and the triangle ...
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37 views

convergence of distribution functions

I have the following assumptions : $\lim_{t \to \infty} F_{t}(a(t)x+b(t))=S(x)\ \forall x \in C(S)$ $\lim_{t \to \infty} F_{t}(\tilde{a}(t)x+\tilde{b}(t))=S^*(x)\ \forall x \in C(S)$ and want to ...
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13 views

Relation between RSD and Mean

Is there any relation between relative standard deviation and mean? In my data there is 3 mean values like 98.1,99.5,97.8 and relative standard deviation is 0.6,0.7,0.8 respectively. Which one is ...
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1answer
27 views

Is difference between two sets of measurements significant?

Consider the following experimental setting: I have two machines $m_0$ and $m_1$ of which I would like to know which one performs better. For this I have set up an experiment to measure the time it ...
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For a normal distribution, find the percentage of data that are between 3.5 standard deviations below the mean and 3 standard deviations above [on hold]

for a normal distribution find the percentage of data that are between 3.5 standard deviations below the mean and 3 standard deviations above the mean
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17 views

How to estimate $\sum_{x=1:n}{xf(x)}$ having $\tilde{f}$

I have an estimator $\tilde{f}(x)$ whose error is at most $\epsilon$, i.e., $\frac{|f(x)-\tilde{f}(x)|}{|f(x)|} \leq \epsilon$. I want to estimate $\sum_{i=1:n}i.f(i)$ with a small error. But if I ...
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26 views

How to get a good approximation or exact value to the average of a group of numbers without storing the numbers in memory?

I am not sure if this is possible, plus I am running on no sleep, so here is what I am asking. Assume I have a list of random numbers. In this instance we will have a list containing $[5, 4, 3, 2, ...
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14 views

Proof of Hammersley and Clifford theorem in Besag's paper

I am reading Besag's paper on Spatial Interaction and the Statistical Analysis of Lattice Systems, see http://www.cise.ufl.edu/~anand/fa11/Besag_Spatial_interaction.pdf. In section 3, it introduces ...
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6 views

Spatially model

Can someone explain to me what a 'spatially lagged autoregressive model' is ? I came across this 'model' by searching new techniques for modeling geographical data.
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14 views

Estimation of real estate

I'm working on a project on estimating the price value of real estate. First I have collected a lot of data (500 000 instances) with details such as postal code, number of bedrooms, build year, ...
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22 views

Continuous time markov chains, is this step by step example correct

I have some questions regarding CTMC... and most importantly whether the step-by-step example I provide below is correct. My main sources about CTMC are: ([1], and [2]). Let's assume 3 possible ...
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1answer
23 views

poisitive definite matrix imply matrix of full rank? [on hold]

Is a positive definite matrix always of full rank? while is given that the characteristic roots are pisitive
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27 views

Total variation inequality [on hold]

In an article I've stumbled upon this inequality: $$ V(f) \leq C(f)s(f) $$ where $f$ is a Lipschitz$(1)$ density with Lipschitz constant $C(f)<\infty$ and support $s(f)$. How can this be derived? ...
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L1 error for scale/translation classes

This is an example given in the article about testability (Devroye and Lugosi 1990). First will introduce my problem, given that we have a density class $\mathcal{F}$ that consists of density ...
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Properties of the essential supremum

In the article about testability of densities (Devroye and Lugosi 1999). They use some properties of the essential supremum I cannot find. First we have to assume that we have a class of density ...
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1answer
31 views

Statistics - Finding the median

Problem : x = 0-4 , 4-10 , 10-18 , 18-30 , 30-40 f(x) = 15 , 35 , 20 , 20 , 10 Finding the median? This is that I did : Cumulative frequency distribution : F(x) = 15 , 50 , 70 , 90 , 100 ...
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1answer
45 views

Exponential of Squared Brownian Motion

Long time lurker, first time posting! Have a problem, that looks familiar but I can't put my finger on it. Need to calculate $\mathbb{E} [\exp(aW_T^2)|F_t]$ where $W_t$ is an $F_t$ adapted standard ...
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What is the distribution of sum of a Rayleigh and a Log-logistic distributed independent r.v.?

Let Z = X + Y. X follows the Rayleigh distribution given by \begin{equation} f_X(x;\sigma_1) = \frac{x}{\sigma_1^2}\exp\left(-\frac{x^2}{2\sigma_1^2}\right), \; x \geq 0 \label{RayleighPDF} ...
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2answers
17 views

Calculating conditional lottery probabilities - and example from DeGroot.

I'm trying to understand this example in Probability and Statistics in DeGroot: http://imgur.com/yjr1vLQ "You learned that the event B = {one of the numbers drawn is 15} has occurred. You want to ...
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1answer
16 views

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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1answer
16 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
27 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
14 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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17 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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25 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
23 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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18 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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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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1answer
59 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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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
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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
24 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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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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46 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
45 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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44 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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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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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
21 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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30 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 ...