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1h
revised Solve $x^{x^x}=-1$
title
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comment Suppose $\xi_1, \xi_2,\ldots$ are i.i.d. random variables with mean $\mu$, variance $\sigma^2$. Form the random sum $S_{N} = \xi_{1}+\cdots+\xi_{N}$.
$\operatorname{var}(E[\xi_{1}+\cdots+\xi_{n}\mid N=n]) = \operatorname{var}(N \mu) = \mu^2 \operatorname{var}(N ) =\mu^2\lambda $
21h
comment sufficient statistics of a sequence of normal random variable
@MichaelHardy: If the variance of $X_i/i$ is $1/i^2$ then its reciprocal (the weights) is $i^2$ so the weighted mean of the $X_i/i$ would be $\dfrac{\sum_i i^2 X_i/i}{\sum_i i^2} = \dfrac{\sum_i i X_i}{\sum_i i^2}$. This is indeed a function of $ \sum_i i X_i$. So this makes sense to me.
1d
comment We all use mathematical induction to prove results, but is there a proof of mathematical induction itself?
And another question on the same theme
1d
revised sufficient statistics of a sequence of normal random variable
y -> x and n
1d
answered sufficient statistics of a sequence of normal random variable
1d
comment sufficient statistics of a sequence of normal random variable
@calculus: you would have $Y_i \sim \mathcal N(\theta,1/i^2)$ which may not make things easier
1d
comment sufficient statistics of a sequence of normal random variable
Your intuition is completely back-to-front: knowing $X_{100}=201$ is more helpful than knowing $X_1=3$ and so $X_{100}$ should have a higher weighting than $X_1$. So intuitively $\displaystyle \sum_{i=1}^n iX_i$ is more likely to be a sufficient statistic, or $\dfrac{ \sum_i iX_i}{ \sum_i i^2}$ if you want an unbiased estimator
1d
comment elementary problem in combinatorics
$R=\{(x,y)\in X\times X$: $x$ and $ y$ have the same remainder when divided by $3\}$?
1d
comment Retrieve the value of x,z and x
Title: "x, z and x", question "x, y and x"
1d
answered Can absolute value functions be moved like this?
1d
answered $x(x^2-2)=0$, The answers are $x = 0, \sqrt{2}$, how do I get there?
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answered Question about usage of $\leq$ in definition of Nash equilibrium
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revised How to remember these probability results?
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2d
answered Clarification on a collared stock being equivalent to a bull spread?
2d
answered Minesweeper probability
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comment Probability that distance of two random points within a sphere is less than a constant
Your first approach will not work when the first point is more than $r-d$ from the centre of the sphere
2d
answered Can someone help me understand this number sequence?
Aug
27
answered Computing $\sqrt[3]{1\,}$
Aug
27
comment Explain instability in Numerics so that I can understand and answer this question that involves roots of a equation
Try an example such as the roots of $(x-7)^2=10^{-20}$ and $(x-7)^2=4 \times10^{-20}$: when $a$ changes by $3 \times 10^{-20}$, the roots change by much more