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Questions tagged [statistics]

Mathematical statistics is the study of statistics from a mathematical standpoint, using probability theory and other branches of mathematics such as linear algebra and analysis.

Statistics is the science of the collection, organization, and interpretation of data. It deals with many aspects of data, which includes the planning of data collection in terms of the design of surveys and experiments. (From Wikipedia)

More specifically, 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 mathematical analysis. (From Wikipedia)

For questions which are more generally about collecting and treating data, it is advised that you post your question on Cross Validated and DSSE.

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Sample Covariance: divide by n or n-1

To obtain the sample covariance, does one divide by $n$ or by $n-1$? I have seen both being used. What is the advantage of using $n-1$? Does it make the covariance unbiased? Or is it so that in the formula for the sample correlation the $n-1$…
user133993
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Probability a Random Variable will assume a value

In a fictional town of ABC, the weather patterns on different days are all independent of each other. Assume that each given day in ABC is sunny with probability 30% and rainy with probability 70%. Let T denote the random variable representing the…
user146772
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Lognormal Distribution

I have a question about MLEs and their regarding to a certain distribution: the lognormal distribution. $$ f_{X}(x ; \mu, \sigma)=\frac{1}{x \sigma \sqrt{2 \pi}} e^{-\frac{(\ln x-\mu)^{2}}{2 \sigma^{2}}}, \quad x>0 $$ And, I have that the expected…
H Cruz
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Moment Generating function proof

Let X have moment generating function M(t), and let v(t)=lnM(t). show that v'(0)=E(X) and v''(0)=Var(X). I know the formula's for E(X) and Var(X), but don't I need an original pdf of X to compute the expected value and variance? How would I show…
user141745
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Multinomial distribution from a contingency table

Over a period of 100 days, weather forecasters issue forecasts for rain on a daily basis. Based on the forecasts and actual observations, you are supposed to help them finding out if the forecasts were any good. A forecast is simply one of the…
user145712
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Confidence intervals, multiple iid variables

If the weight $X$ of bags of cement is normally distributed with a mean of $40$ kg and a standard deviation of $2$ kg, how many bags can a delivery truck carry so that the probability of the total load exceeding $2000$ kg will be $5\%$? The attempt…
user41281
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how to find correlation between 2 arrays of 1's and 0's?

For my case, I have 2 arrays or sets of data, 100 elements, and the values are only 0 and 1. What test or procedure would measure the correlation or independence of the 2 sets? To give an example of the data, suppose one counted if it rained or not…
d l
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Find the probability that the difference between the sample mean and the true population mean wll not exceed 0.5 inch

an anthropologist wishes to estimate the average height of men for a certain race of people. if the population standard deviation is assumed to be 2.5 inches and if she randomly samples 100 mean, find the probability that the difference between the…
user1919987
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What does "central value" mean?

How to calculate central value of the following sets: I'm thinking is the same as the median - is it? $\{-2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1, -5\}$ and $\{-2, -1, 3, 5, 7 , 1, 3 , 6, 2 , -1 \}$
user143368
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Randomized Block Design for repeated trials - Please help

Suppose I measure reaction time of 4 students, initially before any treatment, then after treatment 1, and finally after treatment 2. (Note all treatments will eventually be applied to all students) Also because of potential error with reaction time…
Kenshin
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Fishers Exact test alternative to chi-squared?

Background*strong text* Am analysing results from a questionnaire (n=130). The respondents fall into four categories (A / B / C / D), and each question/statement has 5 possible answers (Likert Scale so Disagree/Agree etc). I want to see if there are…
Harriet
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statistic to measure degree of stationary

I want to claim the time series in figure 1 is more stationary than figure 2. However, [Augmented Dickey-Fuller test asserts http://en.wikipedia.org/wiki/Augmented_Dickey%E2%80%93Fuller_test asserts they are both stationary, at least at 90%…
sinoTrinity
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standard deviation of sums of numbers of different sets

Suppose that I have $n$ different sets of numbers , each containing $m$ different numbers and I can only form sums of $n$ numbers by choosing only one element of each set. Is there an easy way to find the standard deviation of the sums or even an…
user114438
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Switching between two or multiple Poisson processes

Here is the question: Assume that we have $N$ Poisson processes, with arrival rates $\lambda_n, n=1...N$. At the start, we randomly choose, e.g. with equal probability, one Poisson process. Then, when there is an (the first) arrival in this…
user64946
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Median of a sequence of random variables.

Let $\{X_n\}_{n=1}^{\infty}$ be a sequence of i.i.d. random variables such that almost surely $X_n \rightarrow X$. Given just the information above (i.e. no information about distribution) can one determine the median of $X_n$ in the limit as $n…
Celal Bey
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