All Questions
Tagged with expected-value correlation
35
questions
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I don't think this is conditional dependence, so what is it?
I am looking for the name of the following phenomenon. There are three random variables, $X,Y,Z$. We have $P(X,Y) \neq P(X)P(Y)$ and $P(Y,Z) \neq P(Y)P(Z)$. In other words, $X$ and $Y$ are dependent, ...
- 111
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1
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46
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I would like some insight into what I have been working on here
I work in roofing sales which involves door-knocking at the entry level. Our daily numbers are printed in our GroupMe chat for our branch. I took it upon myself to do some analysis on those numbers. ...
0
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78
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Derive the expectation and variance of squared sample correlation: delta-method or else?
I would like to obtain the expectation and variance of the squared Pearson sample correlation ($\operatorname{E}(R_{lk}^2)$ and $V(R_{lk}^2)$) between two random variables $l$ and $k$ following a ...
- 215
3
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1
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127
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Sign of Correlation between $X$ and $f(X)$ for strictly monotonic $f$
This question is a follow up to this question.
Suppose $f$ is strictly increasing. Can we say
$$\text{Cov}(X,f(X))\geq 0?$$
Ben's answer on the aforementioned linked post can be extended to show the ...
- 543
4
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1
answer
143
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Sign of Correlation between $X$ and $\log X$
Suppose $\text{supp}(X)\subseteq \mathbb{R}_{\geq 1}.$ Can we say $$\text{Cov}(X,\log X)\geq 0?$$
On one hand, we can say by monotonicity of log and Jensen's inequality that $$X\geq E[X]\implies \log ...
- 543
0
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0
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30
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What is the relationship between the manifest correlation between ranked variables and the latent, continuous correlation?
Suppose you draw n pairs of observations from a real-valued bivariate distribution. You then convert each observation to its ascending rank order. Given the population correlation for the real-valued ...
- 642
3
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61
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assessing which random sample agrees more with a preferred ranking
I am not a mathematician or a statistician. But, I think the question I have is related to statistics. I will start with a made up example.
If I can grade apples into,say four grades from 1 to 4, one ...
- 33
1
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40
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Expectation of the product of multiple correlated 1-D normal variables [duplicate]
First question: is it possible to have a set of $k$ random variables $\left\{X_i\right\}$ s.t. each $X_i \sim N(0,1)$ individually, and $\text{Corr}(X_i,X_j)=\rho$, $∀i\neq j$?
If those conditions are ...
- 387
0
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597
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Correlation and expected values
Consider two random variables, $x$ and $y$. Denote the correlation between them by $\rho$. Assume that $E[x]$ is also a function of some parameter $\pi$ and is increasing in $\pi$. So if we increase $\...
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5
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2
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Finding correlation coefficient of $X$ and $XY$
Let $X$ and $Y$ be independent random variables with nonzero variances. I'm looking to find the correlation coefficient $\rho$ of $Z=XY$ and $X$ in terms of the means and variances of $X$ and $Y$, i.e....
- 221
5
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75
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The expected value of $\frac{1}{\sqrt{1-r}}$ where $r$ is Pearson correlation
I am looking to unbias the sample statistic $\frac{1}{\sqrt{1-r}}$ where $r$ is a Pearson correlation. The population is assumued binormal with equal variance $\sigma$ and with true correlation $\rho$....
- 249
2
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1
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449
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Observed frequency vs. expected frequency plot interpretation
I'm trying to understand the output of a plot that considers the observed frequency and expected frequency. More or less I've thought that plotting the observed values against the expected values will ...
2
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1
answer
37
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If $cov(x_i,T_i)>0$ can I show $\mathbb{E}[\frac{T'x}{T'T}] > 0$?
x,T are vectors with $cov(x_i,T_i)>0$. Without specifying f(x,T), is it possible to determine the sign of $\mathbb{E}[\frac{T'x}{T'T}]$?
- 111
4
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1
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321
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"Associative" Correlation
For 3 random variables, $X,Y,Z$ all with zero mean
If $E[XY]\ne0$,$E[YZ]\ne0$ then can we say
$$E[XZ]\ne0$$
Alternatively $E[XY]=0$,$E[YZ]=0$ then can we say
$$E[XZ]=0$$
Or even $E[XY]=0$,$E[YZ]...
- 279
1
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1
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135
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Correlation coefficient of x and y
If we have $$ X\sim Poisson(\lambda), Y|X = x\sim Binomial(x+1,p) $$ What is the
correlation coefficient of X and Y?
So I used $$\rho=\frac{Cov(X,Y)}{\sqrt{Var(x)Var(Y)}} = \frac{E[X[E[Y|X]]-E[X]E[...
