query: if $X$ is independent of $Y_1....Y_n$, is it independent of $f(Y_1,..Y_n)$
positive_passages.docid: 29339
positive_passages.text: Are functions of independent variables also independent?
negative_passages.docid: 59106
negative_passages.text: Components of an n-dimensional random variable from a uniform distribution are independent
negative_passages.docid: 125723
negative_passages.text: Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
negative_passages.docid: 118362
negative_passages.text: Determine whether $f_n(x)=\frac{x^n}{\sqrt{3n}}$ for $x \in [0,1]$ is uniformly convergent
negative_passages.docid: 822
negative_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: 83873
negative_passages.text: Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
negative_passages.docid: 154572
negative_passages.text: Continuity of a function at an isolated point
negative_passages.docid: 27072
negative_passages.text: If $X_1,X_2$ are independent beta then showing $\sqrt{X_1X_2}$ is beta
negative_passages.docid: 43667
negative_passages.text: Is $f(x,y(x))$ a function of two variables? If so, how is that possible?
negative_passages.docid: 142855
negative_passages.text: If $A$, $B$ are both pairwise independent of $C$, do we have that $A \cap B$ is also independent of $C$?
negative_passages.docid: 19973
negative_passages.text: If $X$ and $Y$ are independent $N(0,\sigma^2)$, then $X^2+Y^2$ and $X/Y$ are independent?
negative_passages.docid: 155228
negative_passages.text: $X_i, X_j$ independent when $i≠j$, but $X_1, X_2, X_3$ dependent?
negative_passages.docid: 39409
negative_passages.text: $X_1,...,X_n$ be independent RVs and $X_i \perp \mathcal F $ for $1\ \leq \forall i \leq n$. Show that $\sigma (X_1,...,X_n) \perp \mathcal F$
negative_passages.docid: 89186
negative_passages.text: Showing that $\frac{X_{(i)}}{X_{(n)}},i=1,2,...,n-1$ and $X_{(n)}$ are independent for a population with df $F(y)=y^{\theta}$
negative_passages.docid: 121558
negative_passages.text: Showing that $n$ exponential functions are linearly independent.
negative_passages.docid: 89792
negative_passages.text: Let $x,y$ be positive real numbers. Then $x<y$ iff $x^n<y^n$ for all $n\in \mathbb{N}$
negative_passages.docid: 54461
negative_passages.text: Showing independence of random variables