# Questions tagged [iid]

iid is an acronym for independent and identically distributed. Many statistical methods assume that the data are iid; that is, that each observation comes from the same distribution and is independent of other observations.

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### Expectation of inverse of sum of positive iid variables

Let $(X_i)_{i}$ be a sequence of iid positive variables of mean 1 and variance $\sigma^2$. Let $\bar{X}_n = \frac{\sum_{i=1}^n X_i}{n}$. My question is: Can we can bound $\mathbb{E}(1/\bar{X}_n)$ as ...
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### Are i.i.d. random variables always associated with a distribution function? [closed]

It is known that independent and identically distributed (i.i.d.) random variables are mutually independent and each random variable has the same probability distribution as the others. However, is ...
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### i.i.d. assumption for pairwise data generated from clusters

In the context of record linkage, data de-duplication, or entity resolution, we attempt to merge entities that refer to the same thing into a single object. The obvious example is an address database ...
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### SEM-LPA model fit using BIC

I am studying a paper and while I have done a lot of additional reading, I would like some hints on on this issue as I am somewhat stuck. My question is whether a Structural Equation Model of the ...
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### Non-random sampling iid

Suppose I know that 40% of the population are single but my sampling procedure is non-random and skewed towards singles in a way such that in my sample 60% are single. So my data would not be i.i.d. ...
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### $X$, $Y$ independent identically distributed. Are there counterexamples to symmetry of $X-Y$?

That $X-Y$ should be symmetrically distributed for iid $X,Y$ is obvious simply by interchanging the roles of $X$ and $Y$ -- informally we might argue Let $Z=X-Y$ have distribution $F$. The roles of ...
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### $P(X+Y>Z)$ given $X,Y,Z$ are i.i.d random variables

Given $X, Y, Z$ i.i.d random variables the probability $P(X+Y>Z)$ can be found by the following three approaches: $X+Y-Z > 0$ region cuts the $X Y Z$ volume into two equal volumes as $X+Y-Z=0$ ...
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### Distribution notation

beginner here. I've seen in a paper $x\sim NIID(0,1)$ and $y\sim N(0,1)$. This confuses me: to me these both look like standard Normal variables. Can someone explain the difference?
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### When you have two of the same distribution, are they necessarily i.i.d.?

When you have two of the same distribution, are they necessarily independent and identically distributed (i.i.d.)? For example, when you have two from the normal distribution with the same ...