# Tagged Questions

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### Methods for Uncorrelating data - Comparison

I see that both PCA and Cholesky Decomposition could be used for uncorrelating correlated data. When should one be used? What are the assumptions made by each model. When do the methods fail? Are ...
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### Correlation of random variables with joint PDF proportional to $x^{a-1}y^{b-1}(1-x-y)^{c-1}$

The random variables $X$ and $Y$ have joint PDF $$f(x,y)= \frac{\Gamma(a+b+c)}{\Gamma(a)\Gamma(b)\Gamma(c)}x^{a-1}y^{b-1}(1-x-y)^{c-1}$$ where $0 \leq x \leq 1 , 0 \leq y \leq 1, x+y < 1$ where ...
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### Correlation coefficient of i.i.d variables

Let $X_1, X_2, X_3, ...$ be i.i.d variables, and for every $i$ $X_i$ has variance. Define $S_k=\sum_{i=1}^{k}X_i$. Calculate $\rho(S_m,S_n)$ for $m\leq n$. Well, I know it should be $\sqrt{ m/n }$, ...
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### If two Gaussian random variables are uncorrelated, they are statistically independent

I read in a textbook that when two gaussian variables are uncorrelated, then they are statistically independent? How can I prove that?