The area of statistics that focuses on taking information from samples of a population, in order to derive information on the entire population.

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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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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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Inferential statistics question [on hold]

The consumption of sugar is 63 lbs per year. A sample of 16 adults found a mean of 60 lbs per year with a standard deviation of 20 lbs. At a 90% confidence level can we support the 63 lbs population ...
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17 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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26 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
22 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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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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28 views

Iterative Mean, Covariance Algorithm Convergence

The problem is to show that the following iterations converge to the vector $\mu$ and the matrix $\Sigma$. We have data in the form of nx1 vectors $\mathbf{Q}_k$, $1 \leq k \leq N$ where ...
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1answer
22 views

How do I convert non-normal distribution to a normal distribution?

I have the below graph I drew using histogram in Excel but when I got my data and graphed it, certainly it is not a normal distribution. My assignment required me to gather some data and draw normal ...
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1answer
30 views

Mantel-Haenszel $\chi_1^2$ statistic

I was doing a particular example from the book Epidemiologic Research by Kleinbaum(example 15.6) and didn't understood some basic statistical aspect. ...
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19 views

Statistics on a column of values

I have a class project that I am working on as an engineering student but the course is probability and statistics so I don't really know how to make sense or use of what I am learning so I thought of ...
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1answer
26 views

A question about $\chi^2$ distribution

Ok, i have a question but i start with a definition first so that one can get the context. (All variables in question have the same variance and under $H_0$ which we are considering - they have the ...
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1answer
34 views

Method of moments for Beta $(\alpha_1,\alpha_2)$ distribution

I am trying to solve for the first two moments of a Beta$(\alpha_1,\alpha_2)$ distribution. We know that the first moment is equal to: $\mu_1 = \frac{\alpha_1}{\alpha_1+\alpha_2}$ and the second ...
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4answers
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Is it true that $\mathbb E[{\frac{X}{Y}]}={\frac{\mathbb E[X]}{\mathbb E[Y]}}$?

If $X$ and $Y$ are both random variables, does it hold $$\mathbb E\left[\frac{X}{Y}\right]={\frac{\mathbb E[X]}{\mathbb E[Y]}}$$ ??
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What is sampling with unequal probabilities without replacement

sampling without replacement: i know if my sample size is $n$, and if $i^{th}$ unit is drawn then we will not replace the unit in the population , so that in my next draw i can get any unit except ...
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Can I use a z-transformation instead of Welch-t-test

I am not a big mathematician and at the moment I am just refreshing some of my statistical knowledge. So, when doing a students t-test with two independent samples, a precondition is, that both ...
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1answer
16 views

“Approximation” of a maximum likelihood confidence set

I have some trouble constructing the "approximate" set, how can it be defined or calculated? Suppose that three characteristics in a large population can be observed according to the following ...
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1answer
27 views

Alternatives to absolute error?

Let me explain my scenario in which I need to calculate absolute error. Lets say the X is the actual value. And X' is the value of X with some error 'e'. So X' = X + e'. Lets say i = 1 to 10000. I ...
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19 views

UMVUE using complete and sufficient statistic

Let $X_1,X_2,...,X_n$ be a random sample from a normal distribution with mean $\mu$ and variance $\sigma^2$. I showed that $(\bar X,S^2)$ is jointly sufficient for estimating ($\mu$,$\sigma^2$) where ...
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20 views

Maximum Likelihood estimators in linear models

Consider two simple linear models. $y_{1j}=\alpha _1+\beta_{1}x_{1j}+\epsilon_{1j}$ and $y_{2j}=\alpha _2+\beta_{2}x_{2j}+\epsilon_{2j}$ , $ j=1,2,...,n>2$ where $ ...
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1answer
34 views

Finding UMVUE for Poisson distribution using Rao Blackwell

Let ${X_1,X_2,... ,X_n}$ be a random sample from a Poisson distribution with parameter $\lambda$.Let $\gamma(\lambda)=P(X<=1)$. Find UMVUE for $\gamma(\lambda)$. This is my attempt: First I ...
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1answer
25 views

Statistical inference

Ten balls are picked without replacement from a box of 50 balls. All turn out to be red. A argues that the box contains only red balls. B argues that it contains 25 balls each of red and and some ...
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Draw and compare the likelihood using R

The following shows the heart rate (in beats/minute) of a person, measured throughout the day: 73, 75, 84, 76, 93, 79, 85, 80, 76, 78, 80. Assume the data are an iid sample from ...
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19 views

What is the problem with this model parameter estimation algorithm?

In a statistical model with parameters $\theta$ and unobserved laten variables $Z$, the model likelihood is $$L(\theta;X)=Pr(X|\theta)=\sum_ZPr(X,Z|\theta)$$ The standard way to estimate $\theta$ ...
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1answer
22 views

Confidence Intervals with two variables

A random sample of $50$ men shows the following relation between annual income $Y$ (in dollars) and education $X$ (in years): estimator for $Y, (\hat{Y}) = 1200 + 800X $ Average income is $Y = ...
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25 views

Method for detecting anomalies in timeseries?

I am exploring creating alerts for anomalies in a timeseries. Say that I have a graph like this: There are two anomalies here that I would wanted to be alerted on: First, on April 7th with there ...
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35 views

Power testing and a Poisson Distribution

Let $X_1, ..., X_n$ be a random sample from a Poisson distribution with parameter $\lambda$. If $X$ is Poisson with parameter $\lambda$, then $\text{E}[X] = \text{Var}[X] = \lambda$; hence ...
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1answer
35 views

Maximum Likelihood Estimator for a Poisson random variable

$X$ is distributed as a Poisson random variable with parameter $\lambda$ if it has the probability mass function: $f(x; \lambda) = \dfrac{e^{-\lambda}\lambda^x}{x!},\ x = 0,1,2,\ldots$ Find the ...
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19 views

Confidence Intervals and Inferences

I need help with c, as I have attempted a and b already, but believe they help with context. Suppose you took a random sample of 100 accounts in a large department-store chain, and found that the ...
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1answer
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Population Proportions

50% of teens believe that we need to address the problem of climate change. If a random poll of 1500 teens was taken (about the size of the Gallup poll), what is the chance that its proportion would ...
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1answer
34 views

Numerical CDF estimation for complicated random variable

Given a combination $U$ of several random variables $X,Y,Z...$ with known distributions, what is an efficient numerical algorithm to estimate PDF or CDF of $U$, if its CDF, PDF, characteristic ...
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27 views

Parameter estimation of Lorenz system (nonlinear dynamical system)

My problem is as follows. I have to estimate parameters of Lorenz system using given data. Lorenz system is described by following system of ODEs: $$ \frac{dx}{dt} = \sigma(x-y) \\ \frac{dy}{dt} = ...
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Sampling from a graph

Suppose you have a graph $G=(V,E)$ that is unobservable globally and you wish to take a sample from the vertices of that graph to infer something about its global properties from local properties. ...
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1answer
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Model of three mutually exclusive events to be accepted or rejected with confidence .05

According to a genetic model, three mutually exclusive characteristics A, B, C are present with probabilities: P(A) = 0.1, P(B) = 0.2, P(C) = 0.7 In a random sample of size 100, A happens to appear ...
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Show there is no UMP test for $N(\mu,\sigma^2)$

Here's a testing problem. $X_1, \cdots, X_n, indep, \sim N(\mu, \sigma^2)$ where $\mu, \sigma^2$ are unknown. $H_0: \mu \le \mu_0$ vs $H_1: \mu > \mu_0$ where $\mu_0$ is specified. I ...
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Matrix Completion feature vectors

In the noisy matrix completion problem, with enough number of revealed entries say $|E| = nr^2 log(n) $, can we have a bound on the error in the singular vectors of a sub matrix. For, example say ...
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22 views

learning phenomena in bayesian technique

I have identified using bayesian method for my auto tagging application. I am dealing with user facebook post. Post belongs to ...
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1answer
31 views

Question about Logistic Regression - 7

I am currently studying Logistic Regression. I am facing a problem with understand the sentence in the red circle below. I am trying to figure out what he/she means by the sentence. Please let me have ...
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23 views

Question about Logistic Regression - 6

I am studying Logistic Regression and I have come across to understating the paragraph below. I kind of can understand, but it makes me confused when I read the sentence in the red circle, "It also ...
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1answer
26 views

Question about Logistic Regression - 2

How should I tell the difference between those two formulas in the circles below. I am studying logistic regression and I have faced two different formulas from two different documents. I don't know ...
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1answer
19 views

Question about Logistic regression-1

As I am currently studying Logistic regression, but I am still new to this. I have encountered a sentence and a word below in red circles that I can only image but not with my own clear ...
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2answers
36 views

Question about Logistic Regression - 4

I am currently studying on logistic regression. So I have found a document on the Internet explaining about it. Somehow, it explains Bernoulli distribution in the beginning and I am having a problem ...
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1answer
37 views

Whether or not $X_1$,…,$X_n$ are independent and exchangeable

For some n = 1,2,..., let $Y_1$,...,$Y_{n+1}$ denote iid real-valued random variables. Define $X_j$ = $Y_j$$Y_{j+1}$, $\hspace{10mm}$j=1,...,n a) Are $X_1$,$X_2$,...,$X_n$ independent? b) Are ...
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Backwards quadratic programming to infer Q matrix

Consider the standard QP problem: $\arg\min \frac{1}{2}x^TQx +c^Tx$ Say I know the optimal $x$ for a large number of solutions to this problem with various (known) $c$, and identical (unknown) $Q$. ...
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3answers
45 views

Question about English sentences in statistics?

Can somebody help me interpreting the red circled sentences in planer English? I understand "We view $y_i$ as a realization of a random variable $Y_i$ that can take the values of one and zero" but ...
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Expectation maximazation with variant lenght at observing data

Imagine one loaded dice. Based on EM algorithm How could we compute how much it loaded if we introduced 1) variant length on rolling 2) uncertainty values (see-quality) on seeing 1,2,3,4,5 or 6? ...
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Multiplying a binary predictor variable with another predictor variable.

Is it completely valid, to have an equation with a certain amount of variables, where two of the variables multiply each other? For example, I want to have an equation $Y = B_0 + B_1X_1 + B_2X_2 ...
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22 views

Question about Logistic Regression - 5

Can somebody give me a clear explanation about logistic regression in bold below? Logistic regression can be binomial or multinomial. Binomial or binary logistic regression deals with situations in ...
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1answer
19 views

Understand the English paragraph on association rule.

I am currently studying Association Rule Pattern Mining. I am reading the explanation on wikipedia about it. Somehow, I feel like I have a problem in understanding the paragraph below. Can somebody ...
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1answer
29 views

Is the sum of predicted y values equal to the sum of actual y values?

Say I have a set of points Y and I want to accuratly predict the values of Y by using three variables X1,X2,X3. Hence my equation is Y=intercept + C1*X1 + C2*X2 + C3*X3 After performing linear ...