If $A $ and $B$ are independent R.V., will $A^2$ and $B$ be independent?
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
18967
Linear independence of $\sin(x)$ and $\cos(x)$
102777
Is $G^{(X, Y)} = (G^X)^Y?$ ($A^B$ just means that $B$ is mapped to $A$)
17032
If $ab=ba$, Prove $a^2$ commutes with $b^2$
158852
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 $|a_1| > 3$?
119782
Suppose $S_1 =\{ u_1 , u_2 \}$ and $S_2 = \{ v_1 , v_2 \}$ are each independent sets of vectors in an n-dimensional vector space V.
27072
If $X_1,X_2$ are independent beta then showing $\sqrt{X_1X_2}$ is beta
30017
Orthogonality and linear independence
138212
Please help me prove: $v(a+b)\leq v(a)+v(b)$, and $v(ab)\leq v(a)v(b)$ where $v(x)=\inf{\{\vert x^n \vert}^{1/n}: n\in\mathbb{N}\}$
43282
Why do $n$ linearly independent vectors span $\mathbb{R}^{n}$?
65224
Prove that if $a^2 = a$ for all elements of the ring $R$, then $R$ has characteristic 2. Is the converse of the statement true?
158406
$A,B$ be Hermitian.Is this true that $tr[(AB)^2]\le tr(A^2B^2)$?
111800
If $a|c$ and $b|d$, is it true that $ab|cd$?
58329
Show that $y_1$ and $y_2$ are not Linearly Independent
126988
Are two independent events $A$ and $B$ also conditionally independent given the event $C$?
142855
If $A$, $B$ are both pairwise independent of $C$, do we have that $A \cap B$ is also independent of $C$?
15191
If $a^2$ divides $b^2$, then $a$ divides $b$