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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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Finding the solution to this MLE problem

Suppose $X_1,X_2,\ldots,X_n$ be a random sample of distribution with probability density function $$f(x\mid\theta) = \theta x^{\theta-1},\quad 0\lt x \lt 1,\quad 0\lt \theta \lt \infty$$ how can i find MLE of parameter $θ$? My working is like…
lakshmen
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condition on $a_1,\ldots,a_n$ so that $a_1X_1+\ldots+a_nX_n$ is an unbiased estimator of the mean

Let $X_1,\ldots, X_n$ be a random sample from a population with mean $\mu$. What condition must be imposed on $a_1,\ldots,a_n$ such that $$a_1X_1+\ldots+a_nX_n$$ is an unbiased estimator of $\mu$. I am new to statistics and am not sure how to…
Slugger
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What are degrees of freedom for different regression models?

The dispersion formula for Fisher's kriterium is: $D_{\tilde y}=\frac {1}{n-k} \sum\limits_{1}^{n} \left[\frac {y_{mi}-y(x_{mi})}{y(x_{mi})}\right]^2$ depending on type of regression model used. $y(x_{mi})$ is the value got from the regression…
Nikolay Yasinskiy
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How to do the M-step in the EM algorithm?

I have been trying to implement the EM-algorithm in order to segment stores into k-clusters. What I already did was derivation of the complete-log-likelihood and also performed the E-step. Where it goes wrong is the M-step. I showed that I need to…
Tim
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Tchebysheff's theorem

Let k≥1. Show that, for any set of n measurements, the fraction included in the interval $\bar{y} − ks$ to $\bar{y} + ks$ is at least $(1−1/k^2)$. This result is known as Tchebysheff's theorem. Hint: $s^2=(1/(n−1))\displaystyle\sum\limits_{i=0}^n…
Username Unknown
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Playing On A Saturday

So, I am trying to solve this question: James and John are playing football/soccer on a sunny Saturday. They are practicing their penalties and play 3 games. In each game, they either score or they miss. How many possible ways can their games turn…
River Uzoma
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Confusion about One equality about Marginal likelihood

When I checked Wikipedia about Marginal likelihood, I find an equality of the form: $$ p(a\mid b)=\int p(a\mid c)\cdot p(c\mid b)\,dc $$ and it's valid because the parameter c is marginalized/integrated out. However, when I tried proving its…
Sol
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Statistics reduce

First of all, I'm sorry I'm a complete statistics iliterate, I promise I'm going to get into it after the summer (I need them for my job actually). Because of this I'm not sure about the name of what I'm asking about, I will explain and you tell me…
MeGusta
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Statistical correlation in Assassin's Creed: Rebellion

The point of this question is only to check that I still know how to do statistics. So in Assassin's Creed Rebellion, there are 9 character classes. And each class has a unique resource which can be turned into a weapon or armor etc. In the previous…
ControlAltDel
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How to find the expectation a gamma distributed variable given the sum of i.i.d. gamma-distributed variables?

Let $X_1,\cdots,X_{10}$ be i.i.d. random variables, where $X_i$ is from Gamma$(\alpha,\beta)$ with $\alpha>0$ and $\beta>0$. I want to find $E(X_1|\sum_{i=1}^{10} X_i=10)$. Here's my attempt: Since $X_i$ are i.i.d., $E(X_1|\sum_{i=1}^{10}…
Accept Cookies
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Why does evaluation of Mode include special cases when the max. frequency is at the extremes or when there are irregularities in distrubution?

Preface I was reading the textbook Fundamentals of Mathematical Statistics by S.C. Gupta and V.K. Kapoor and I came across exceptional cases where mode is simply not the observation with the highest frequency. The book states for ungrouped data:…
Gudimella Jayanth
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Finding the regression line given the mean, correlation and standard deviation of $x$ and $y$.

So we have $100$ observations for $(x, y)$. The mean of $x$ is $1.06$, and for $y$ it is $3$. The standard deviation is $0.52$ for $x$ and for $y$ it is $1.13$. the correlation between $x$ and $y$ is $0.89$. In the question we are told to: •…
Raditz
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monotone likelihood ratio property of truncated distributions

What are the conditions that truncated normal distributions satisfy the monotone likelihood ratio property? How about other truncated distributions?
user12586
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Is there a mistake in the coin toss example in Mandelbrot's book "The Misbehavior of Markets", while he introduces the Hurst Exponent?

In his book "The Misbehavior of Markets", Mandelbrot introduces the Hurst exponent with a coin toss example. He says that when you toss coins for a large number of times, you can get consecutive runs of heads or tails. For instance, in a $100$…
Mete V
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Any relationship for repeated results for tossed coin?

I tossed coin (fair) 10 times and collected data as follows:- H H T H H T H T H H what I did added "repeat" in observation if previous toss was same; like H (Repeat) H T H (Repeat) H T H T H (Repeat) H "(Repeat)" if last toss is same…
Rodeny
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