query: If two random variables are independent does that mean if one of them is squared then the independency still exists?
positive_passages.docid: 29339
positive_passages.text: Are functions of independent variables also independent?
negative_passages.docid: 151302
negative_passages.text: If $X$ and $Y$ are independent random variables, with $Z = \min(X,Y),$ prove that $Z^2\sim\chi^2(1),$
negative_passages.docid: 147866
negative_passages.text: If X,Y and Z are independent, are X and YZ independent?
negative_passages.docid: 84203
negative_passages.text: Let $X_1$ and $X_2$ are independent $N(0, \sigma^2)$ random variables. What is the distribution of $X_1^2 + X_2^2$?
negative_passages.docid: 104225
negative_passages.text: Difference between two independent binomial random variables with equal success probability
negative_passages.docid: 138798
negative_passages.text: Independence and conditional distribution
negative_passages.docid: 75035
negative_passages.text: Law of Total Probability/Independence question
negative_passages.docid: 9665
negative_passages.text: Proof of the independence of the sample mean and sample variance
negative_passages.docid: 39378
negative_passages.text: Moment generating functions/ Characteristic functions of $X,Y$ factor implies $X,Y$ independent.
negative_passages.docid: 79457
negative_passages.text: Geometric random variables $X_1:G(p_1)$ $X_2:G(p_2)$ $X_3:G(p_3)$ are independent, prove the following :
negative_passages.docid: 154091
negative_passages.text: Is there any counterexample to show that $X,Y$ are two random variables and $E(X\mid Y)=E(X)$, but $X$ and $Y$ are not independent.
negative_passages.docid: 45220
negative_passages.text: Proving the sum of two independent Cauchy Random Variables is Cauchy
negative_passages.docid: 3888
negative_passages.text: What is the difference between independent and mutually exclusive events?
negative_passages.docid: 62665
negative_passages.text: If X and Y are continuous random variables, then the random vector (X,Y) is a continuous random vector?
negative_passages.docid: 62007
negative_passages.text: Durrett Example 1.9 - Pairwise independence does not imply mutual independence?
negative_passages.docid: 150141
negative_passages.text: Showing $X$, $Y$ are not independent but $\operatorname{Cov}[X, Y] = 0$
negative_passages.docid: 142966
negative_passages.text: Intuition behind independence and conditional probability