131 Why is Euclidean distance not a good metric in high dimensions? 73 How can I calculate $\int^{\infty}_{-\infty}\Phi\left(\frac{w-a}{b}\right)\phi(w)\,\mathrm dw$ 70 Why does the correlation coefficient between X and X-Y random variables tend to be 0.7 52 Variance of product of multiple independent random variables 49 How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance?

### Reputation (38,997)

 +10 How can I prove mathematically that the mean of a distribution is the measure that minimizes the variance? +10 Why squaring $R$ gives explained variance? +10 What are i.i.d. random variables? +10 Median of mixture of two Gaussian distributions with equal weights

### Questions (3)

 18 Maximum value of coefficient of variation for bounded data set 17 Bound on moment generating function 16 Is joint normality a necessary condition for the sum of normal random variables to be normal?

### Tags (235)

 1k probability × 224 456 mathematical-statistics × 66 617 normal-distribution × 115 332 correlation × 39 575 distributions × 103 296 independence × 59 513 self-study × 140 276 conditional-probability × 54 477 random-variable × 82 214 machine-learning × 16

### Bookmarks (3)

 17 Which is largest, of a bunch of normally distributed random variables? 13 Is it possible that two Random Variables from the same distribution family have the same expectation and variance, but different higher moments? 6 Understanding proof of McDiarmid's inequality