If $c_i=a_ib_i, c_j=a_jb_j,$ $a_i$ and $a_j$ are independent, $b_i$ and $b_j$ are dependent, what about $c_i$ and $c_j$?
31133
Functions of Independent Random Variables
101320
How to tell $i$ from $-i$?
110327
How to do this question that talks about dependency of x
33633
Re:$ (a,b,c,d)=(pr+qs, qr-ps,pr-qs,ps+qr) $
142229
Prove that if $V \cap \text{Span}\{u_1, u_2,...,u_k\} = \{ 0\} $, then $Au_1, Au_2,...,Au_k$ are linearly independent
68137
Independence and conditional independence between random variables
138798
Independence and conditional distribution
21726
Show that if $(b,c)=1$, then $(a,bc)=(a,b)(a,c)$.
107540
how to prove that $abc$ and $cba$ do not necessarily have the same order?
64395
If $v_1,...,v_r$ are eigenvectors that correspond to distinct eigenvalues, then they are linearly independent.
111800
If $a|c$ and $b|d$, is it true that $ab|cd$?
40609
Prove that $f(X)$ and $g(Y)$ are independent if $X$ and $Y$ are independent
85167
When A and B are of different order given the $\det(AB)$,then calculate $\det(BA)$
17928
How to prove the following expression does not depend on x?
19973
If $X$ and $Y$ are independent $N(0,\sigma^2)$, then $X^2+Y^2$ and $X/Y$ are independent?
111191
Show that $P_i$ and $\sum_i P_i$ being idempotent implies $P_i P_j=\delta_{ij}$
131026
Covariance and independence?