Mathematics Stack Exchange
Mathematics Stack Exchange

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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(correction)Sampling distribution homework

I'm doing my homework and i dont have the answers, can someone say if its correct? "Let the population X, defined by X~Ber(p); Find The sampling distribution of an RV. X¯=1n∑ni=1Xi where Xi is the obtained value from an extraction with reposition of…
PlayMa256
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Existence of kth moment

Degroot makes a statement in his textbook: It can be shown that for every positive integer $k$, $$\int_{-\infty}^{\infty}|x|^ke^{-(x-3)^2}\,dx<\infty$$ Can someone show me how I might prove this statement?
David
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x in the range of a random variable $X$ implies the pdf $f_X(x)>0$

Let $\mathcal X$ be the range of a continuous random variable $X$. Next, let $x\in\mathcal X$. If $f_X$ is the pdf of the random variable $X$, how can I prove that $f_X(x)>0$?
David
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Prove (n choose k)(p)^(k)(1-p)^(n-k) = 1

I am taking a statistics course and found this question in my textbook. I am trying to incorporate the binomial theorem into the proof, but am hitting a wall. Any suggestions would be greatly appreciated. Update: Is this answer sufficient or would…
Greta
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Finding out missing observation $a$ and $b$

The mean of $a,b,8,5,10$ is $6$ and the variance is $6.8$. find out value of $a$ and $b$ I tried something like this: $$\bar{x}=6=\frac{a+b+8+5+10}{5}$$ $$7=a+b$$ Then i have put the value in the formula of variance $$variance\…
Freddy
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How to find a moment estimator?

Suppose you have $X_1,\ldots,X_{20}$ $f(x|\theta) = 0.1(1+\theta x)$ for $-1
lord12
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Introduction to statistics

Let $X$ be uniformly distributed on $[a,b]$. Find a function $f$ such that $Y=f(X)$ is exponentially distributed with parameter $1$. How do I do this?
user109707
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If F is a cumulative distribution function, then $\lim_{x\to\infty}F(x)=1$

Let $F$ be a c.d.f for a random variable X and let $$x_1
David
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Motivation behind definition of mean deviation

So I got to start working on some statistics notes and at first everything seemed intuitive, the concepts were pretty basic. But then they got a little more complicated. So I do know the neat idea behind the mean deviation which is basically that it…
user155181
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Human size and number of A-alleles

Imagine that the human size is influenced by a gene with two different alleles (gene variants) $A$ and $a$. Concerning this topic you have collected the following data: $\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \text{proband} & 1 & 2 & 3 & 4 &…
mathfemi
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Basic statistics problem

i have a small statistics problem: The time spent by students to solve an exam, following a normal distribution, has a mean of 80 minutes, and a standard deviation of 20 minutes. .. and asks: What's the minimum time that 30% of the students spent on…
Inside
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What is the minimal depth of a decision tree if it grows to full size?

If we grow a classification tree with $n$ samples and a $p$-dimensional predictor variable, what is the minimal depth of a decision tree if it grows to full size? There is an answer saying that The maximal number of observations at each depth $d$…
hxhxhx88
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Bias of maximum likelihood estimator of an exponential distribution

The maximum likelihood estimator of an exponential distribution $f(x, \lambda) = \lambda e^{-\lambda x}$ is $\lambda_\text{MLE} = \frac n {\sum x_i}$; I know how to derive that by taking the derivative of the log likelihood and setting it equal to…
fool
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Finding out sample variance

Find out the variance of first 50 even natural number? I know variance $\sigma^2=\frac{\Sigma(x_i-\bar{x})^2}{50}$ I have also find $\bar{x}=2550/50=51$ by using Arithmetic Progression. But now what to do further i have no clue.
Freddy
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What probabilty density do I use with poisson processes?

For this question: Given a poisson process with on the avg "a" arrivals per unit time, find the probability that there will be no arrivals during a time interval of length t, namely, the probability that the waiting times between successive…
nubela
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