# Tagged Questions

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### How to test whether the variance of two distributions is different if the distributions are not normal

I'm studying two geographically-isolated populations of the same species. Inspecting the distributions, I see that both are bimodal (there's some seasonality to their occurrence), but the peaks in one ...
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### Standard error from correlation coefficient

Many studies only report the relationship between two variables (e.g. linear or logistic equation), $n$, and $r^2$. I want to use these reported statistics to reproduce this relationship with its ...
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### When does a distribution not have a mean or a variance?

I believe I read today a phrase which went something like this: If a distribution has a mean and a variance ... So I guess that means some distributions do not have means or variances? I fiend ...
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### Is variance computed on weekly basis the same as variance computed on daily basis?

I have a proportion value computed on a weekly basis with 95% confidence interval. Now I want to get the proportion on a daily basis, instead. Assuming the values are uniformly distributed, I divided ...
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### When can the variance be written as a function of expectation?

What kinds of distribution have variance as a function of expectation, i.e. let $X$ be a random variable of a distribution, $Var(X) = f(E(X))$ for some function $f$ ? Sufficient conditions including ...
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### How to calculate the variance of the GED distribution?

The density of the GED distribution is given by \begin{align} GED(l;\mu,\beta,\nu)&=\frac{\nu \exp\left[-(\frac{1}{2}) \left|\frac{l-\mu}{\beta \lambda}\right|^\nu \right]} {\lambda ...
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### Mean and variance of number of tries required

So the question states that I'm trying something with an 85% chance of success, if I don't succeed I try again until I do. What is the mean and variance of the number of tries necessary until I ...
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### Simple homework question about normally distributed variables

The question states: Consider a set of random variables $X_i$, where $i=1,...n$. Each $X_i$ is normally distributed with mean $0$ and variance $1$, i.e. $X_i$ are $\mathcal N(0,1)$. What is ...
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### Standard deviation of weighted sums of random distributions with weights random but fixed

Let $a,b,c,d$ be independent normally distributed random variables. I'm aware that the following distributions: $$c a + d b$$ $$(c+d)a$$ both have the same standard deviation ($=\sqrt{2}$ if ...
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### Distribution which has maximum or minimum variance for a given entropy

We know that the normal distribution has the maximum entropy among all continuous distribution on $\mathbb{R}$ for a given variance. I wonder what's the opposite, i.e. what distribution has the ...
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### How can I find distribution from mean and variance

If I know the mean and variance of a discrete random variable $\in \{0,1,\dots \}$, How can I find the distribution?
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### Var(X) is known, how to calculate Var(1/X)?

If I have only $\mathrm{Var}(X)$, how can I calculate $\mathrm{Var}(\frac{1}{X})$? I do not have any information about the distribution of $X$, so I cannot use transformation, or any other methods ...
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### What is the expectation of exponential of the product of two random variables?

I am looking for examples of probability distributions that would allow me to characterize the distribution (at least approximately) and to compute the first two moments exactly of: $$e^{aXY}$$ ...
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### Repeatedly rolling a six sided die four times and summing the highest three results gives you a distribution with what mean and standard deviation?

Repeatedly rolling a six sided die four times and summing the highest three results gives you a distribution with what mean and standard deviation? I've only taken AP statistics, but I would like to ...
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### Something like Central Limit Theorem for variance and maybe even for covariance?

CLT states in short, that sum/mean of random iid variables from almost any distribution approaches normal distribution. I failed to find information about asymptotic behavior of sample variance when ...
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### How does one measure the non-uniformity of a distribution?

I'm trying to come up with a metric for measuring non-uniformity of a distribution for an experiment I'm running. I have a random variable that should be uniformly distributed in most cases, and I'd ...
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### How many samples should be taken to capture the mean and variance of the original set with given error?

I have a set $S$ of $N$ real numbers. I wanna calculate the mean $m$ variance $v$ of $S$. But since $N$ is too large, I do not want to use all of the numbers. Instead, I would like to sample $n$ ...
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### Understanding “variance” intuitively

What is the cleanest, easiest way to explain someone the concept of variance? What does it intuitively mean? If one is to explain this to their mom or child how would one go about it? It's a concept ...
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### How to create a ratio distribution from samples?

Ok, let's try again. The context of the original question is given below, but perhaps it helps to focus on the statistical aspect to get an answer. What I got is a number of measurements in unit t. ...
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### How do you derive the conditional variance for $s^2$, the OLS estimator of $\sigma^2$?

I just need a little bit of a push in the right direction. I'm working my way through Hayashi's Econometrics and hit a snag in section 1.4. Review question 7 asks: Show that, under Assumptions ...
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### Distribution of a ratio of two proportions

$A$, $B$, $C$, $D$ are positive integers. $$A \sim Binomial(p_1, A+B)$$ $$A+C \sim Binomial(p_2, A+B+C+D)$$ My variable of interest is $p_1/p_2$ Could one analytically compute a distribution ...