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Questions about covariance, a measure of (linear) association between two random variables.

2 votes

If the Covariance between $(X,Y)$ is finite, then the second moment of $X$ is finite?

Let $X, Y$ be random variables such that $$X = \begin{cases} 1.9^i, & i = 1, 2, 3, ... \\ 0, & \text{otherwise}\end{cases} \\ P(X = i) = \begin{cases} (\frac 12)^i, & i = 1, 2, 3, ... \\ 0, & \text{ …
  • 1,008
0 votes
1 answer
48 views

Covariance of a Portfolio with a Stock in that Portfolio

In the provided solution, this is said: The covariance of $X$ with the portfolio, since $X$ is uncorrelated with the other two stocks, is $0.4(0.27^2) = 0.02916$. What justifies this statement? …
  • 1,008
2 votes
Accepted

Finding the covariance of coordinates of a circle.

You might be able to get a little bit more insight with a picture: Shown is a circle with $r=2$ around the origin. By definition of $\sin\Theta$ and $\cos\Theta$ you can see that $(X_u,Y_u) = (r\co …
  • 1,008
1 vote
1 answer
30 views

Variance of return of a portfolio of stocks

Here's a derivation my textbook gives for the variance of the return $R_p$ of a portfolio of stocks with arbitrary weights $x_i$: $$ \mathrm{Var}(R_p) = \mathrm{Cov}\left( R_p, \sum_{i=1}^n x_iR_i \ri …
  • 1,008
0 votes
Accepted

Expected Value, Variance, and Covariance of Card Game

First of all, yes, $\mathsf{E}[\cdot]$ is a linear operator, so your justification for $\mathsf{E}[I+II]$ holds. For $\mathsf{E}[I*II],$ let $X=I$ and $Y=II$. Then $I*II = XY$. $$\mathsf{E}[XY] = \s …
  • 1,008