query: Independence of random variables composed of independent random variables with standard normal distribution
positive_passages.docid: 822
positive_passages.text: Given that $X,Y$ are independent $N(0,1)$ , show that $\frac{XY}{\sqrt{X^2+Y^2}},\frac{X^2-Y^2}{2\sqrt{X^2+Y^2}}$ are independent $N(0,\frac{1}{4})$
negative_passages.docid: 19034
negative_passages.text: Covariance of products of dependent random variables
negative_passages.docid: 42017
negative_passages.text: What is the distribution of the Euclidean distance between two normally distributed random variables?
negative_passages.docid: 84376
negative_passages.text: How to compute probabilities of normally distributed variables?
negative_passages.docid: 9665
negative_passages.text: Proof of the independence of the sample mean and sample variance
negative_passages.docid: 90411
negative_passages.text: $P(X_1 < \min(X_i,\ldots, X_n))$ across different normal random variables
negative_passages.docid: 44892
negative_passages.text: Marginal, joint, and conditional distributions of a multivariate normal
negative_passages.docid: 31133
negative_passages.text: Functions of Independent Random Variables
negative_passages.docid: 61101
negative_passages.text: Sum of two independent normal distributed random variables
negative_passages.docid: 112001
negative_passages.text: The sum of $n$ independent normal random variables.
negative_passages.docid: 86729
negative_passages.text: Are squares of independent random variables independent?
negative_passages.docid: 133729
negative_passages.text: Sum of normal independent random variables with coefficients
negative_passages.docid: 100600
negative_passages.text: Linear combination of two dependent multivariate normal random variables
negative_passages.docid: 108335
negative_passages.text: Approximate order statistics for normal random variables
negative_passages.docid: 118867
negative_passages.text: Independence of Gaussian variables
negative_passages.docid: 146005
negative_passages.text: pdf of a member of a sequence of dependent random variables
negative_passages.docid: 154309
negative_passages.text: Probability question of independent random varaibles