query: If $X_1, X_2 $ are independent RVs. then are ${X_1}^2$ and ${X_2}^2$ are independent?
positive_passages.docid: 86729
positive_passages.text: Are squares of independent random variables independent?
negative_passages.docid: 127378
negative_passages.text: Is $2^\alpha=2^\beta\Rightarrow \alpha=\beta$ a $\sf ZFC$-independence result?
negative_passages.docid: 33907
negative_passages.text: The product of a normal and Rademacher variables, independent from each other
negative_passages.docid: 145039
negative_passages.text: Algebraic independence over $\overline{\mathbb Q}$ and over $\mathbb Q$
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: 63598
negative_passages.text: Is every separately continuous function on $R^2$ continuous?
negative_passages.docid: 102529
negative_passages.text: Prove that the set $\left\{ x, Ax, \dots, A^{k-1} x \right\}$ is linearly independent
negative_passages.docid: 100656
negative_passages.text: $2\times2$ matrix $A$ such that $A$ has one independent eigenvector while $A^{2}$ has two independent eigenvectors
negative_passages.docid: 109228
negative_passages.text: Prove that $v, Tv, T^2v, ... , T^{m-1}v$ is linearly independent
negative_passages.docid: 158852
negative_passages.text: If $\{v_1, v_2, v_3\}$ is an orthonormal basis of $\mathbb{R}^3$ and $v = a_1v_1 + a_2v_2 + a_3v_3$, can we have $|a_1| > 3$?
negative_passages.docid: 142229
negative_passages.text: Prove that if $V \cap \text{Span}\{u_1, u_2,...,u_k\} = \{ 0\} $, then $Au_1, Au_2,...,Au_k$ are linearly independent
negative_passages.docid: 76884
negative_passages.text: Are $X$ and $X+Y$ independent, if $X$ and $Y$ are independent?
negative_passages.docid: 150282
negative_passages.text: If $A$ is independent of $B$ and $C$ then why is it not necessarally independent of $B\cap C$?
negative_passages.docid: 132386
negative_passages.text: Show that $(\mathbb{Q}^*,\cdot)$ and $(\mathbb{R}^*,\cdot)$ aren't cyclic
negative_passages.docid: 95928
negative_passages.text: Independence and orthogonality
negative_passages.docid: 8291
negative_passages.text: If $n$ vectors are linearly independent, is their span $\mathbb{R}^n$?
negative_passages.docid: 31898
negative_passages.text: Sufficient conditions for $x, Ax, A^2x, ...$ being linearly indepedent