0
votes
1answer
50 views

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 ...
1
vote
1answer
29 views

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 ...
0
votes
2answers
62 views

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 ...
1
vote
1answer
84 views

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 ...
1
vote
1answer
103 views

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 ...
0
votes
5answers
184 views

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?
2
votes
2answers
437 views

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 ...
4
votes
1answer
809 views

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: $$ e^{aXY} $$ ...
4
votes
2answers
365 views

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 ...
2
votes
1answer
228 views

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 ...
4
votes
2answers
1k views

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 ...
1
vote
1answer
119 views

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 $n$ ...
20
votes
5answers
3k views

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 ...
2
votes
0answers
221 views

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. ...
1
vote
1answer
387 views

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 ...
-4
votes
1answer
261 views

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 ...
4
votes
2answers
98 views

Distribution of a random segment on a string

I have a linear string of unit length, and I randomly sample two locations a and b from Uniform(0, 1). Then I cut the string at these two locations to get a sub-string. What is the distribution for ...
6
votes
2answers
1k views

How to parameterize the ratio of two normally distributed variables, or the inverse of one?

Problem: I am parameterizing distributions for use as a priors and data in a Bayesian meta-analysis. The data are provided in the literature as summary statistics, almost exclusively assumed to be ...