All Questions
15 questions
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Is the variance of the mean of a set of possibly dependent random variables less than the average of their respective variances? [closed]
Is the variance of the mean of a set of possibly dependent random variables less than or equal to the average of their respective variances?
Mathematically, given random variables $X_1, X_2, ..., X_n$ ...
- 139
1
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1
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57
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Variance of $X + \alpha^\top Y$ where $X$ is a scalar random variable and $Y$ is a random vector [duplicate]
Consider a scalar random variable $X\in\mathbb{R}$, a vector random variable $Y\in\mathbb{R}^n$ and a constant (non-random) vector $\alpha\in\mathbb{R}^n$. I want to compute
$$
\mathbb{V}[X + \alpha^\...
- 667
1
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1
answer
61
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If $X\in\{0,1\}$, then $\frac{cov(X,Y)}{Var(X)}=\mathbb{E}(Y|X=1)-\mathbb{E}(Y|X=0)$
If $X\in\{0,1\}$, then $\frac{cov(X,Y)}{Var(X)}=\mathbb{E}(Y|X=1)-\mathbb{E}(Y|X=0)$
I have no idea what to address with the conditional expectation part.
Thank you for any comments, someone has ...
- 331
1
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0
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31
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Understanding Covariance after Variance (visually)
2 Points i understood from variance derivation-
A) For calculating Variance we do not subtract (or mod add), but rather sum squared all points' differences from the mean.
B) Variance of 1,2,3 will be ...
- 11
0
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1
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440
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Expresion for Var(X/Y)
I am suggested the following formula and I can't find some reference on this expression :
$$\text{Va}r(X/Y)=E(X^2/Y^2)-E^2(X/Y)=\text{Cov}(X^2，1/Y^2)+E(X^2)E(1/Y^2)-(\text{Cov}(X,1/Y)+E(X)E(1/Y))^2$$
...
user226073
2
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1
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360
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What can be deduced about the covariance between f(x) and f(x + K) for constant K?
The question concerns transformations of a random variable $X$ by a function $f$. I’d like to understand whether there are conditions that could make:
$$\operatorname{covar}(f(X), f(X + K) ) \geq \...
- 115
1
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1
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63
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Understanding covariance
I came across following problem:
A discrete random variable $P$ takes values $-3,-2,0,2,3$ with probability $0.2$. Let $Q=P^2$ be another random variable. What is covariance of $P$ and $Q$?
I solved ...
- 225
0
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0
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31
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Variance/covariance computations in a simple probability weighted estimator
My recent homework included a problem where I had to to show that:
$\frac{\delta^2}{p^2} Var(\hat{p}) - \frac{2 \delta}{p} Cov(\hat{\delta} + \frac{\delta}{p} (\hat{p} - p), \hat{p})$ < 0,
where $\...
2
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1
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239
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Will change in standard deviation impact covariance?
If we increase the degree of standard deviation of one variable, does it affect covariance of two variables?
Example, two variables are there, A & B, the covariance of A & B is 100, and the ...
6
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1
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232
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What is the meaning of $\sqrt{\mathrm{var}(X)\mathrm{var}(P)-[\mathrm{cov}(X,P)]^2}$?
What is the meaning of the quantity:
$$\varepsilon=\sqrt{\mathrm{var}(X)\mathrm{var}(P)-[\mathrm{cov}(X,P)]^2}$$
Is there, for example, a geometric explanation? Is there a term for it in statistics?
- 161
0
votes
0
answers
94
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Conditional Covariance Problem
Suppose we have independent (not necessarily identical) normally distributed random variables X, Y. If we're given that, upon sampling each variable, X is some multiple a of Y (i.e. x = ay), what is ...
1
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1
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225
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Variance and covariance inequality
Given a real-valued random variable $X$, is
$$2\mathbb E[X] \mathrm{Var}(X) \geq \mathrm{Cov}(X, X^2)$$
true?
Any pointers for how to tackle this problem would be immensely helpful.
- 549
1
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0
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114
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Variance of bivariate normal distribution plus normal distribution
Problem:
$W = -27 + 0.3X + 0.45Y + E$
The pair $\begin{bmatrix} X \\ Y \end{bmatrix}$ behaves like a bivariate normal with vector of averages $\begin{bmatrix} 156 \\ 86 \end{bmatrix}$ and ...
- 107
2
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2
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4k
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Variance of a sum of identically distributed random variables that are not independent
I am "new" to probability/statistics and I was hoping someone could verify that this is correct. Let $Y_1,\ldots,Y_n$ be random variables that follow a common distribution with mean $\mu$ and variance ...
- 23
0
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0
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833
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Joint Density and Covariance between Two Random Variables with the same Mean and Variance
This seems like a deceptively simple question, (and it perhaps is and I am missing something) but I could not find anything on this.
Q1)
Are there any general results / relationships to get the Joint ...
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