# Questions tagged [data-sufficiency]

questions regarding sufficiency of information.

49 questions
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### Using statistics in petroleum engineering [closed]

How can engineers use mathematical statistics to determine relationship between number of wells and oil, gas and water production?
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### Party Invitations Problem [closed]

There is a party on some Sunday next year, it is open to all. a)Everyday at some point, a person comes and drops a slip with contact details in a dropbox. b)A person on a given day could comeback ...
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### can minimal sufficient be independent of observation?

(1)part(a): can minimal sufficient be independent of observation? $\\$ let $X$ is one observation from $U(\theta, \theta+1)$, $\theta \in \{0,\pm1 ,\pm 2 ,\cdots \}$ $T=\lfloor X \rfloor$ is ...
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### Hogg Intro to Mathematical Statistics Sufficient Statistic Notation Question

When introducing the notation of a sufficient statistic, Hogg uses a peculiar sort of notation at the bottom of page 381 of the 7th edition textbook: given the statistic $$Y_1 = u_1(X_1,X_2,...,X_n)$$ ...
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### Finding Sufficient statistic

Let $X_1,\dots X_n$ be an i.i.d sample from the distribution with frequency function $$P(X=x) = \left(\frac{\theta}{2}\right)^{|x|}(1-\theta)^{1-|x|}$$ for $x = -1,0,1$. Use the factorization ...
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### Minimal sufficient statistics for uniform distribution on $(-\theta, \theta)$

Let $X_1,\dots,X_n$ be a sample from uniform distribution on $(-\theta,\theta)$ with parameter $\theta>0$. It is easy to show that $T(X) = (X_{(1)},X_{(n)})$ is a sufficient statistic for $\theta$ ...
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### Significant figures between SI and non-SI units

This question on Chem.SE addresses the question I feel more suitable for math.SE: A person is running 10 km, and wikipedia states a US land mile corresponds to 1609.344 m. Would it be more sensible ...
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### sufficient statistics to estimate the unknown parameters

I am a beginner in statistical inference and am learning sufficient statistics. As far as I know the distributions conditional on the sufficient statistics doesn't depend on the unknown parameters. I ...
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### Find a sufficient statistic for $σ^2$ with $μ$ known, where $X_i$ is a random sample from $N(μ,σ^2)$

Find a sufficient statistic for $σ^2$ with $μ$ known, where $X_i$ is a random sample from $N(μ,σ^2)$ I was able to find a sufficient statistic for $μ$ with $σ^2$ known, but I'm stuck on finding one ...
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### Let $\theta >0$ be unknown and suppose that $(X,Y)$ is uniform over the triangular region with vertices at $(0,0)$,$(\theta, 0)$, and $(0,\theta)$.

Let $\theta >0$ be unknown and suppose that $(X,Y)$ is uniform over the triangular region with vertices at $(0,0)$,$(\theta, 0)$, and $(0,\theta)$. Let $(X_i,Y_i)$ be iid as $(X,Y)$. Find a one ...
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### Show that $T$ is not a sufficient statistic

Let $X_1\: , X_2$ a random sample for $N(\theta ,1).\:$ Show that $\:T=X_1 + 2X_2$ is not a sufficient statistic. I've tried to prove it by contradiction: I assumed that $T$ is sufficient. That ...
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### File Compression Statistics

Statically, how is the compression of a file possible? As in, a file n bytes long can have $2^{n*8}$ (the 'times 8' part is because there are 8 bits in a byte). So, if you decrease the size then ...
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### What are the coordinates of point P? SweSAT Data sufficiency

The points $P = (x_1, y_1)$ and $Q(3, 4)$ are on the line $y=kx+m$. What are the coordinates of point $P$ ? Given $m = -2$ $P$ is on the line $x=2$ We need both information together to solve the ...
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### SweSAT Data Sufficiency

A product has undergone two price increases with the same percentage, ie by x percent each time. How big was the increase in percent each time? ( 1 ) The total price increase was 450 dollars (2) ...
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### sufficient statistics of a sequence of normal random variable

If $X_1, X_2\ldots,X_n$ are independent variables with $X_i \sim \mathcal N(i\theta,1)$, $\theta$ is an unknown parameter. What is a one dimensional sufficient statistic $T$ of this sample? I have a ...
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### Find the sign of $a,b,c$ in $ax^2+bx+c$ given the graph and a coordinate on it.

So my first approach was that, we see that there are $2$ roots. And one is negative and one is positive. $a$ would be evidently positive. The positive one's modulus is bigger than the negative one's. ...