All Questions
20 questions
0
votes
0
answers
468
views
How to derive the short cut version of variance calculation for probability distribution
How to derive from formula 2 to 3?
- 365
1
vote
3
answers
151
views
Calculate the variance of a distribution analytically
I want to calculate the variance of a certain distribution.
I have a rectangle that is getting shifted to the right (i.e. shear transformation). To obtain the distribution I am computing the value of ...
- 113
0
votes
0
answers
428
views
What is the distribution of cross-sectional volatility?
Assume we have a set of $N$ random variables with known multivariate distribution $\boldsymbol{X}\sim\mathcal{N}(\boldsymbol{\mu},\boldsymbol{\Sigma})$, and a series of realisations $\{\boldsymbol{X_t}...
0
votes
1
answer
466
views
Find variance of an estimator
Let X1,X2..,Xn a random sample from a population X having distribution function
$f(x;θ) = θx^{θ - 1}$ if 0 < x < 1
Where θ > 0 is a parameter. Is the estimator $θ = \frac{x̄}{1 - x̄}$ of θ ...
- 217
0
votes
0
answers
136
views
Sampling distribution of exponential sample variance (formal not empirical)
Addressing this problem:
Let $X_1, ..., X_n$ be iid exp($\theta$) with pdf,
$f(x)=\frac{1}{\theta}e^{-\frac{x}{\theta}}$. What is the distribution of the sample variance?
This is to be done by ...
- 9
0
votes
0
answers
17
views
Sampling Distribution of Exponential Sample Variance (Formal, not Empirical) [duplicate]
Addressing this problem:
Let X1,...,Xn be independent identically distributed exponential variables with parameter θ, i.e. with pdf, f(x)=(1/θ)*exp(−x/θ). What is the distribution of the sample ...
- 9
5
votes
1
answer
477
views
Variance of $Z = X_1 + X_1 X_2 + X_1 X_2 X_3 +\cdots$
Here the $X_i$'s are i.i.d. and such that convergence in distribution for the infinite sum, is guaranteed. Probably the easiest case is when $X_i$ has a Bernouilli($p$) distribution, then $Z$ has a ...
4
votes
1
answer
303
views
Variance of beta distribution (fastest way)
Suppose a Random variable $X \sim \mathrm{Beta}(a,b)$
Find the $\mathrm{Var}( \frac{X}{1-X} ) $
My initial approach is to calculate $\mathrm{E}( \frac{X}{1-X} ) $ and $\mathrm{E}( [\frac{X}{1-X}]^...
- 213
3
votes
3
answers
851
views
$P(\lvert X - \mu\rvert \geq \sigma)$ as a measure of tailedness
I know that one of the standard measures for the "tailedness" of a distribution is kurtosis, i.e. fourth standardized central moment $\frac{\mu_4}{\sigma^4}$. This measure is sort of intuitive to me: ...
- 133
4
votes
1
answer
2k
views
On finding the asymptotic distribution of the sample variance using the delta method
This is an exercise I am stuck on.
Given an IID sample $X_1, \dots, X_n \sim N(\mu, \sigma^2)$ with $\mu \ne 0$ let
$$S_n^2 = \frac{1}{n} \sum_{i = 1}^n ( X_i - \overline{X_n})^2$$
be the sample ...
- 1,465
10
votes
1
answer
17k
views
if 2 random variables have exactly same mean and variance [duplicate]
If two continuous random variables have exactly the same expected value and variance, do they always have the same distribution?
- 103
4
votes
1
answer
2k
views
What is the correct way to add and subtract skewness from a distribution?
If I recall correctly, we can add and subtract variance if variables are independent, and have a mean of 0.
I have two distributions that are summed up: (a) one with high variance, low skewness and ...
- 143
1
vote
1
answer
27
views
Establishing Groupings Based on Behavior
Consider the following scenario:
Collection of user data from a community site similar to StackExchange reveals that certain users tend to "agree" with other users; e.g., when participating in the ...
- 111
3
votes
2
answers
1k
views
How can variance be non constant for Bernoulli and Poisson
Until now I had learned that the variances of Bernoulli and Poisson random variables are $p(1-p)$ and $λ$ and that for fixed $p$ and $λ$, these variances are constant.
Now, introducing glm, my course ...
user110848
-2
votes
2
answers
111
views
I need help to show that $E(\sum x)=\sum E(x)$ [closed]
If for a normal distribution $E(x)=\overline{x}$ and if we have $E(\overline{x})=E(\frac1N\sum_{i=1}^Nx_i)=\frac1N\sum_{j=1}^N\left(\frac1N\sum_{i=1}^Nx_i\right)_j$ how can then $E(\overline{x})=\...
- 566
2
votes
1
answer
396
views
If X~Exp(λ), what is the expected value of Y=X²?
I am trying to compute this using the integral definition of expected value but I don't think I am doing it right as I am getting a very hard integral that I can not solve.
When computing $\mathbb{...
- 61
3
votes
1
answer
155
views
Can you derive the distribution of the Gaussian variance estimator without using moment generating functions?
Given a dataset of Gaussian i.i.d. $X_i's$, we can show that the maximum likelihood estimates for this Gaussian distribution's mean and variance are given as:
\begin{align}
\hat{\mu} &= \frac{1}{...
- 141
10
votes
4
answers
2k
views
Inverse function of variance
For a given constant number $r$ (e.g. 4), is it possible to find a probability distribution for $X$, so that we have $\mathrm{Var}(X)=r$?
- 231
3
votes
1
answer
71
views
How to calculate the correlation coefficient from minimal distributional assumptions?
Let random variables $X_1,X_2,\ldots,X_n$ satisfy $$(X_i,X_j)\stackrel{d}{=}(X_1,X_2)\quad \forall i, j$$
(that is, these variables are identically distributed and all their bivariate marginal ...
- 109
37
votes
2
answers
8k
views
Distributions other than the normal where mean and variance are independent
I was wondering if there are any distributions besides the normal where the mean and variance are independent of each other (or in other words, where the variance is not a function of the mean).
- 17.9k