# Questions tagged [central-limit-theorem]

For questions about the central limit theorem, which states: "Given certain conditions, the mean of a sufficiently large number of iterates of independent random variables, each with a well-defined mean and well-defined variance, will be approximately normally distributed." (Wikipedia)

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### What intuitive explanation is there for the central limit theorem?

In several different contexts we invoke the central limit theorem to justify whatever statistical method we want to adopt (e.g., approximate the binomial distribution by a normal distribution). I ...
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### T-test for non normal when N>50?

Long ago I learnt that normal distribution was necessary to use a two sample T-test. Today a colleague told me that she learnt that for N>50 normal distribution was not necessary. Is that true? If ...
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### Central limit theorem for sample medians

If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a ...
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### Is MLE of $\theta$ asymptotically normal when $(X,Y)\sim e^{-(x/\theta+\theta y)}\mathbf1_{x,y>0}$?

Suppose $(X,Y)$ has the pdf $$f_{\theta}(x,y)=e^{-(x/\theta+\theta y)}\mathbf1_{x>0,y>0}\quad,\,\theta>0$$ Density of the sample $(\mathbf X,\mathbf Y)=(X_i,Y_i)_{1\le i\le n}$ drawn from ...
### How many of the biggest terms in $\sum_{i=1}^N |X_i|$ add up to half the total?
Consider $\sum_{i=1}^N |X_i|$ where $X_1, \ldots, X_N$ are i.i.d. and the CLT holds. How many of the biggest terms add up to half the total sum ? For example, 10 + 9 + 8 $\approx$ (10 + 9 + 8 $\dots$ +...