Prove independence of two random variables.
822
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 $N(0,\frac{1}{4})$
154309
Probability question of independent random varaibles
138962
$X$ is a random variable, if $\Bbb E(X^2)=1$ and $\Bbb E(X)\geq a>0$, prove that $\Bbb P(X\geq\lambda a)\geq(a-\lambda a)^2$ for $0\leq\lambda\leq 1$.
41100
Density of sum of two independent uniform random variables on $[0,1]$
121853
$X$,$Y$,$Z$ mutually independent implies $X+Y$ independent of $Z$
94077
Proof of linear independence of $e^{at}$
124936
Help with a Probability Proof
31133
Functions of Independent Random Variables
153393
Is there a *simple* example showing that uncorrelated random variables need not be independent?
39409
$X_1,...,X_n$ be independent RVs and $X_i \perp \mathcal F $ for $1\ \leq \forall i \leq n$. Show that $\sigma (X_1,...,X_n) \perp \mathcal F$
145294
Independence of linear combination of multivariate distribution
20728
Proof that this is independent
105691
Showing that the sample mean and variance are independent by showing two distribution are the same
49896
A criterion for independence based on Characteristic function
59106
Components of an n-dimensional random variable from a uniform distribution are independent
124973
Discrete Uncorrelated Dependent Random Variables
142325
Two independent geometric random variables - proof of sum