2
votes
Accepted
Is the cosine angle between two R.V. an (approximation) not equality to the correlation coefficient?
Hint:
$X \cdot Y$ is a random variable.
$\text{Cov}(X,Y)$ is an expected value.
---- addendum ----*
There is some confusion of terminolgy in your post.
If $\bf X , \bf Y$ are two random vectors (in ...
- 33.5k
1
vote
Accepted
Compute expected value from two dimensional normal distribution
The term in the exponent of $f(x,y)$ can be written as
$$\begin{split}-\frac 18\left[4x^2+8x(y+3)+6(y+3)^2\right] &= -\frac 12 \left[x^2+2x(y+3)+\frac 32(y+3)^2\right]\\
&=-\frac 12\begin{...
- 10.1k
1
vote
Accepted
When independent variables covary (not correlate) in the regression, why this happen?
It is because R cannot handle decimals that small. The model should be
$y=1/999999iv1+1/999999iv2$ for model 2. If you do iv1=99999v1 and iv2=99999v2, you will get a significant interaction much fewer ...
- 10.1k
1
vote
Variance and covariance problem
I'm also getting that $\mathbb{Var}(X)\geq 2$.
First of all, $$\begin{eqnarray*}2&=&\mathbb{Cov}(X,Y) \\&=& \mathbb{E}(XY)-\mathbb{E}(X)\mathbb{E}(Y) \\&=& \mathbb{E}(XY)-\left(...
- 7,542
1
vote
Accepted
Covariance, and the Taylor expansion for the expected value of a linear function of random variables
Expectation is linear, and therefore
$$
\mathbb{E}[\theta] = \mathbb{E}[U(X)]-\mathbb{E}[U(Y)]
$$
regardless of whether $U,Y$ are independent or not. They could be arbitrarily correlated, this would ...
- 64.2k
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