# Tagged Questions

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### Countermonotonicity and minimum linear correlation coefficient

In an example exercise they question whether it is possible to construct a bivariate distribution of $LN(0,1)$- and $LN(0,4)$-distributed random variables, where $LN(\mu,\sigma^2)$ is the log normal ...
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I am trying to get my head wrapped around this article in Wikipedia. The first definition given there is the covariance of a probability measure $\mathbf{P}$: $$\mathrm{Cov}(x, y) = \int_{H} \langle ... 0answers 28 views ### Correlation: How to extend it from pairs to further random variables? How can one determine the correlation coefficients (or their intervals) between n standard-normal random variables X_i, i=1,...,n, when X_i correlates with X_{i+1} with correlation ... 1answer 128 views ### Covariance and Correlation Suppose there were m married couples, but d of these 2m people have died. Regard the d deaths as striking the 2m people at random. Let X be the number of surviving couples. Find: a) E(X) b) Var(X) ... 1answer 133 views ### Correlation of Indicator Variables Show that for indicator random variables I_A and I_B of Events A and B: Corr(I_A, I_B) = Corr(I_A^c, I_B^c) = -Corr(I_A, I_B^c) = -Corr(I_A^c, I_B) Deduce that if A and B are ... 1answer 279 views ### Invariance of the correlation coefficient under linear transformations Show that for arbitrary random variables X and Y, and constants a,b,c,d with a and c nonzero,$$ \mathrm{Corr}(aX+b,cY+d) = \begin{cases} \mathrm{Corr}(X,Y)\quad&\text{if }a \text{ and ...
Suppose I have three uncorrelated random variables $X, Y$ and $Z$ (discrete or continuous) such that $$\newcommand{\Cov}{\mathrm{Cov}}\Cov(X,Y)=0;\quad \Cov(Y,Z)=0;\quad \Cov(X,Z)=0 \tag{\ast}$$ I ...