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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How many white balls are there in the box most probably?

There are n balls in a box. Some of them are white. A ball drawn from the box turns out to be white. How many white balls are there in the box most probably? Alright, well i know there are originally ...
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17 views

divide amount spent equally

Me and my friend needs to divide the amount spent equally. He brought food worth of 20 dollars and I brought worth of 130 dollars. Now I need to divide this money equally so that we both spend equal ...
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1answer
30 views

tricky integrating ranges x1-x2

So, we know the sum of n i.i.d. exponential(lambda) is gamma(n,lambda). But I am looking at a problem with X1-X2. So I get the joint dist of z=x1-x2 and w=x2. Then I integrate out w on range 0 to ...
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1answer
24 views

Probability and Stats - understanding the sample variance formula

I am trying to find the sample standard deviation of a sample space of n=100. I am doing this by using the formula for sample variance: $$(1/n-1)\sum_{i=1}^{100}(Yi - Ybar)^2$$ and then taking the ...
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1answer
90 views

How to calculate peakiness or uniformity in histogram?

I have a histogram with 20 bins ranging from -1 to 1 with an interval of 0.1. I would like to know if the histogram distribution is uniform or is peaked. I want to compare several such histograms and ...
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1answer
43 views

Finding the 99% of a normally distributed graph

The heights of adults are normally distributed with a mean of 187.5 cm and a standard deviation of 9.5 cm. A standard doorway is designed so that 99% of adults have a space of at least 17 cm over ...
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1answer
32 views

Prediction error in least squares with a linear model

In the classical linear model with $$Y=X\beta +\epsilon,$$ where $Y \in \mathbb{R}^n$ is the observation, $X\in \mathbb{R}^{n\times p}$ is the known covariates, $\beta \in \mathbb{R}^p$ is the ...
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1answer
374 views

Pearson's Chi Squared / Cochran–Mantel–Haenszel test analog to N-way ANOVA

A test was given to two sets of students, CONTROL and EXPERIMENT, that had question A and question B. I want to know if students who got question A right were more likely to get question B right, and ...
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3answers
271 views

Statistics - Calculating Mean given standard deviation and percentage.

This is one of our homework problems for Statistics. I'm really stuck on this one, and it would be great if someone could show me how to solve this, or at least set up the equation. The weights of ...
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0answers
12 views

conditional expected value of the maximum of n normally distributed variables

What is the conditional expected value of the maximum of n normally distributed variables x_i, conditionally on exceeding some threshold z: That is, for x=max(x_1,..x_n), the probability that x will ...
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11 views

How to calculate Kappa for segmented images using two judges images

I have two reference images representing the two judges, and i have my segmented image. Now i want to calculate the Kappa of my segmented image. As i understood from this paper that i should have the ...
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13 views

Finding test of critical region for sum/variance of normal distributions

Let $Y_1,....,Y_n$ denote independent, identically distributed random variables such that $Y_1$ has a normal distribution with mean $\theta$ and standard deviations $\theta$, where $\theta$ > 0. ...
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18 views

interpretation of fractional moments?

The first moment is the mean (central tendency), the second the variance (dispersion), etc. If you calculated the $3/2$ moment, what would it mean? Or (say) the $2.35$ moment? They CAN be ...
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1answer
28 views

Survival function in terms of the hazards

Let $T$ be a discrete random variable assuming values $x_1<x_2<\ldots$ with probability $f(x_i) = \text{Pr}\left\{T=x_i\right\}$. Show that the survival function $S(t)=\prod_{i:x_i\leq ...
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0answers
5 views

Truncated expectation comparison

What is the condition for two continue distribution F and G (with same support) to guarantee E[x|x>c] under dist F >= E[X|x>c] under dist G? c is a constant. Thanks!
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8answers
4k views

If a lottery has 300 tickets, shouldn't I win every 300 times I play

Suppose I play a lottery that has 300 tickets. I can only buy one ticket per draw. Statistically speaking, shouldn't I win once every 300 draws? Is it more complicated than this? Edit This question ...
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0answers
8 views

2D histogram from points on spherical surface of spherical coordinate system

What are the options available for creating a 2D histogram of points distribution on a sphere? Both polar angle (phi) and azimuth angle (theta) are known, and radial distance is 1.
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3answers
48 views

In how many ways can 88 trees be planted in a circle [closed]

How many different ways are there to plant 88 trees in the shape of a circle? to be more specific the circumference of a circle
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0answers
20 views

Showing distribution has a $\chi^2$ distribution with df = n

Let $X_1,X_2,....,X_n$ denote independent identically distributed random variables such that $X_1$ has density $p_1(x;\theta)$ where $\hspace{15mm}p(x;\theta) ...
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1answer
17 views

How many samples from a poisson distribution until you have X unique values?

Suppose you have a population of non-negative integers normally distributed with a mean of 0 standard deviation of a large value (say around 1 Million). Is there a formula that tells you how many ...
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1answer
26 views

What is the formula for the birthday problem?

What is the formula for the birthday problem? I can't seem to find JUST the formula. I don't care how it works at this point, I just want to know what to do. Can someone please just tell me? Most ...
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1answer
33 views

Unbiased sample standard deviation of a custom/unknown probability distribution

Hi i must determine the unbiased sample standard deviation of an unknown probability distribution.I dont have the data of the full population so i must work with a sample. Now according to Wikipedia ...
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17 views

density of statistic

Let $X^1$ ... $X^n$ be a random sample coming from a distribution with density : $p(x)=\begin{cases}2\theta^2/x^3, \text{if} \ x\geq 0 \\ \\ 0, \text{if} \ \ x<0 \end{cases}$ Let us denote the ...
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18 views

The relation between non-Gaussianity and statistical independency

I have read in Wikipedia article which is talk about ICA , that the definition of statistical independence can be achieved by maximization of non-Gaussianity , my ...
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1answer
31 views

MLE of Urn Without Replacement Problem

An urn has W white balls where W is unknown. Suppose that R=5 Red balls are added to the urn and then a random sample of N=10 balls is selected. But this time, Suppose that we continue to draw balls ...
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2answers
321 views

If the covariance matrix is $\Sigma$, the covariance after projecting in $u$ is $u^T \Sigma u$. Why?

I read in this answer that: If covariance matrix is $\Sigma$, the covariance after projecting in $u$ is $u^T \Sigma u$. I fail to see this, how do I get the covariance of a set of points after ...
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1answer
20 views

variance negatif?

whether the variance of the parameters obtained from the inverse observed information matrix can be negative? I am looking for a variant of the parameters in a way to make "observed information ...
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1answer
26 views

Digital Uncertainty

What am I doing? I am calculating wind velocity $v$ from the mean of n samples of differential pressure $\Delta P$ using the following formula: $$v=\frac{1}{n}\sum\limits_{i=1}^n\sqrt{\frac{2\Delta ...
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1answer
13 views

What statistical analysis to use on a list of dates?

I suffer from migraines and for many years I've kept a log of each attack. I now want to do some analysis on the dates of each attack to see if there are any patterns. I intend to check the ...
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0answers
20 views

Statistics and Some Information Challenge

relation between two attribute x,y is $y=\alpha\beta^{-x}$. According to 8 experiments these information were gained. what is the estimation of ( $\alpha, \beta$) using Least Square Error? it's 2010 ...
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1answer
22 views

statistics basic question on covariance

anyone would help me in a basic example? a fair coin is tossed, n times. X is the number of Head and Y is the number of Tails. what is the COV(X,Y).
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16 views

about moments of a uniform distribution on a high-dimensional ball

I need to understand how the following integrals depend on the dimension $d$; the result should be about a (negative) power of $d$. Let $\mathbb{B}^d$ be the $d$-dimensional ball of radius $1$, ...
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4answers
97 views

Conditional Probability matching socks

A drawer contains eight different pairs of socks. If six socks are taken at random without replacement, compute the probability that there is at least one matching pair among these six socks. Hint: ...
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2answers
61 views

In composition of two mappings, can the outer mapping access the arguments of the inner mapping?

In composition of two mappings, can the outer mapping access the arguments of the inner mapping? Here is an example to illustrate my question and my thought. E.g. $f: \cup_{n \in \mathbb N} \mathbb ...
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1answer
23 views

Cumulative Poisson Distribution Question

For the following question I figured that the expected time between successive arrival is the mean = 1/10 per hour (or 1 per 6 minutes). My question is regarding the second part; does the fact that ...
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1answer
20 views

Hypergeometric Distrbution issue

So I am trying to figure out some probabilities using hypergeometric distribution, and I am a little confused on one part I am trying to figure out. I know how to figure out what the probability is ...
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1answer
240 views

comparing two normally distributed random variables

In a large corporation, people over age thirty have an annual income whose distribution can be approximated by a normal distribution with mean 60,000 and standard deviation 10,000. The incomes of ...
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2answers
27 views

Expected value equal to expected value of expected value squared?

I am trying to rederive the canonical expression for variance $V[X] = E[X^2] - E[X]^2$. What I don't understand is the second line. If you multiply E( ... ) by the last term, wouldn't you get ...
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2answers
15 views

Conditional statestic

I have this exercise. A batch of 500 containers for frozen orange juice contains ten that are defective. Two are selected, at random, without replacement from the batch. (a) What is the ...
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2answers
42 views

Conditional probability of having blue eyes based on hair color [closed]

In a class, 60% of students have brown hair, 30% have blue eyes, and 10% have both. A student is randomly selected. Given that the student had brown hair, what is the probability that they also had ...
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3answers
26 views

There are 98 working lightbulbs in a batch of 100, and 2 non-working ones. How many ways could a sample

of 5 be selected that contain /at least/ 1 of the broken bulbs? So far, I have tried only 1 method, as it's the only one I've been taught, but I don't know if I am doing it right. I tried doing ...
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0answers
53 views

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11?

Two dice are rolled. If the sum is greater than 8, what is the probability that it is 11? I'm not sure if this question is asking for conditional probability or just 2/10...
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2answers
23 views

Derivative of Survival Function

I am trying to get through statistical survival analysis - sadly I only have high school math. I have the following equation: $ S(t) = Pr\{T ≥ t\} = 1−F(t) = \int_t^\infty f(x) dx$ $f(x)$ is the ...
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1answer
11 views

Given MTTF and Number of Items, how to calculate failing parts with Time?

I am wondering how to make use of MTTF Here is the situation, I am given an MTTF for an item type x and a certain demand for that item in the next 25 years, say 100 parts that will be in operation ...
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0answers
14 views

Predictiction / extrapolation of values

I have some data in which I collected for hour. Its the CPU utilization of a particular machine while it was decoding a video file. I need to predict the value for the same fr the next 2 hours and ...
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1answer
42 views

the difference between statistically independent and linearly independent?

what is the difference between statistically independent and linearly independent concepts?
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1answer
17 views

Normaliztion of a random variable.

Suppose I have a column of data(random variable) and I need to transform that data in to normal random variable how do I do it?
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1answer
16 views

Kernel density estimation including measureed uncertainty

I am trying to plot the distribution of a measured variable from a scientific experiment, in this case a velocity. After making a simple histogram, I have been reading this, ...
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1answer
18 views

Is this form of distribution considered Bimodal or Uniform?

Would this form of distribution be considered Bimodal or Uniform? I have been searching through distribution images and the Bimodal distributions generally appear to refer to a pair of Normal ...
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1answer
46 views

Understanding an application of Fubini's theorem

I'm going over some lecture notes for a course in statistical theory. There is a "proof" that the density for a $k$-dimensional multivariate normal random variable (with non-singular covariance) is, ...