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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.

37109 questions
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What is the expected value of sample mean?

I have a simple question. $X$ is a random variable with mean $μ$, and there is a sample of size $n$: $X_1, X_2, \cdots, X_n$. Then what is the expected value of the sample mean $\overline{X}$? This is what I thought: $$\overline{X} =…
Matheoo
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Calculating expected value of sample standard deviation

How do we calculate $$ \begin{align}E[S]&=E\left[\sqrt{\frac{1}{n-1}\sum_i(x_i-\bar{x})^2}\right]\\&=E\left[\sqrt{\frac{1}{n-1}} \sqrt{\sum_ix_i^2-n\bar{x}^2}\right]. \end{align}$$ I am asking this question out of curiosity mostly because it is…
matt
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Why is $\ln(1-x) \approx -x$ when $x$ is small?

I saw this in a proof for the Central Limit Theorem: $\ln(1-x) \approx -x$ when $x$ is small It seems to be true when I plug in small values of $x$. But why does it work?
foobar
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Calculate skewness and kurtosis fast

Calculating the variance and the central moments with a dumb calculator can be a pain. My question is if I have the standard deviation is there a quick way to calculate the skewness and the kurtosis
JDizzle
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Moment Generating Function for a discrete random distribution

(Discrete uniform distribution) A discrete random variable is said to be uniformly distributed if it assumes a nite number of values with each value occurring with the same probability. If we consider the generation of a single random digits, then…
Alex
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Statistics: Predict 90th percentile with small sample set

I have a quite small data set (on the order of 8-20) from an essentially unknown system and would like to predict a value that will be higher than the next number generated by the same system 90% of the time. Both underestimation and overestimation…
bukzor
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Find the asymptotic distribution of the MME and MLE.

Question: Let $X_1, ..., X_n$ be i.i.d random variables with the density function $$f(x|\theta) = (\theta+1)x^\theta, 0≤x≤1$$ Find the asymptotic distribution of the MME and MLE. My Guess: I know from doing a previous part in the question that…
AZ0987
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Mean Squared Error Maximum uniform distribution

Let $X_1,\ldots,X_n$ be Uniform Distributed Random variables on $[0,\theta]$ and let T be $\max\{X_1,\ldots,X_n\}$ an estimator for $\theta$. I derived that the $F_T(x)=(\frac{x}{\theta})^n$ for $0
user408856
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Sampling Distribution of sample mean for Poisson Distribution

I am particularly struggling with part b, I don't know where to begin. For part a, I think the answer is that the sampling distribution is a Poisson(n$\lambda$).
Jackdaw
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Can something be statistically impossible?

Does it make sense when people say "statistically impossible"?
CallumDA
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Why are squares chosen as a weighting method for quantifying the deviations from a mean?

Reading about variance and it occurred to me that this squaring business seems to be used many places in statistics. I think I understand that the square is used to help "weight" values which are further from the mean more heavily, so they don't…
paIncrease
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Calculating parallel program's execution time

I am trying to calculate the probable execution time of a highly parallelizable program, where the execution's 70%-80% can run in parallel. I read about the topic, but mostly people mention simple situations, but I have another condition the…
Sabiwww
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Finding the MLE for parameter $\theta$ from distribution of the form $e^{-|x-\theta|}$

this is my first post so I apologize if the formatting is a little rocky. I'm currently going through "Probability and Statistics" 4th ed by DeGroot/Schervish, and I was wondering if somebody could help me out on two related problems (7.5.10,…
Chase Uyeda
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Sufficient statistic for Uniform distribution.

We are given that $ X_i \sim U( 0 , \theta )$ where $\theta$ is unknown. We need to find a sufficient statistic. First we write the conditional distribution : $$ f( x_1 ,\ldots ,x_n \mid \theta ) = \frac 1 {(\theta)^n}, \text{ where } ( x_i \leq…
User9523
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What is the chance of an event happening a set number of times or more after a number of trials?

Assuming every trial is independent from all the others and the probability of a successful run is the same every trial, how can you determine the chance of a successful trial a set number of times or more? For example, You run 20 independent trials…
Franks
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