# Tag Info

### Is Central Limit Theorem about multiple samples or just one?

First let's be clear about the meaning of the word sample. A sample contains a(n often large) number of (often but not always independent) observations from a population. In some fields of study, the ...
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### Probability that X > Y when X ~ N(0,2) and Y ~ N(0,1)

The fact that the distribution of $X-Y$ has mean $0$ does NOT imply that $\mathbb{P}(X-Y<0)$ and $\mathbb{P}(X-Y>0)$ are equal. So for the last step it is not enough that $X-Y$ has mean $0$, you ...
• 266
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• 81.4k
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### What is the substantive meaning of one statistical test is more powerful than another?

If a test has any power and always returns $p=1.0$ that implies that the sample size is too small to be doing statistical testing. Power of competing tests is compared at the null, to show that the ...
• 95.7k
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### Bivariate normal covering circles and ellipses

What you want is the radius $r$ such that the cdf $P(\sqrt{X^2+Y^2}\leq r)=\alpha$ for some alpha. It is clear that $P(\sqrt{X^2+Y^2} \leq r)=P(X^2+Y^2 \leq r^2)$, and it is easier to work with the ...
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### Finding conditional expectation of conditional distribution

Is this the correct approach? I don't feel confident, because $s$ and $\tilde{s}$ is correlated and the term above does not include any information regarding that. The $s$ and $\tilde{s}$ are not ...
• 82.4k
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### Let $S = X + U, T = X + V$ for ind.normal r.v $X, U,V$. Is it possible to find $a, b$ real numbers such that $\mathbb{E}[X|S,T] = \mathbb{E}[X|aS+bT]$

Without loss of generality, assume $X, U, V \text{ i.i.d. } \sim N(0, 1)$ (in general the analysis below requires the joint normality of $(X, U, V)$). The joint normality of $(X, U, V)$ and ...
• 20.5k
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### Normality test using normal Q-Q plot and histogram

While I agree with whuber's comment that this is unlikely to be useful, and while you don't say why you are doing this, I think that, nevertheless, something useful can be said. Of course, if you have ...
• 125k
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### What are bounded distributions? and can a bounded distribution hold the normality assumption?

First, yes, a bounded distribution has ... well, bounds. This is a case where the natural meaning of the phrase is accurate. Second, yes, the Normal distribution has no bounds. That's part of the ...
• 125k
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### Fitting data: "most normal residuals" vs maximum-likelihood

Since there's a good amount of discussion in the comments I will demonstrate why the normality of the residuals is a poor measure. I will use Shapiro Wilks test instead of KS, as KS needs to be ...
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