$X$, $Y$ be independent geometric random variables and let $U$ be the smaller of $X$ and $Y$, and put $V = X - Y$. Show $U$ and $V$ independent.
117907
A question regarding independence of $\min{\{X,Y\}}$ and $X-Y$ when $X,Y$ follows iid geometric distribution
67219
Can anyone help clarifying the geometry in this probability, random variables question.
36374
Exercise 1.6.3 from Alon & Spencer's *The Probabilistic Method*: prove that $Pr[|X-Y| \leq 2] \leq 3 Pr[|X-Y| \leq 1]$ for i.i.d. real RVs $X$ and $Y$
14664
Sum of indepedent random variables and a constant
124827
Show that $Y\sim N(a+A\mu,AVA^T)$
154091
Is there any counterexample to show that $X,Y$ are two random variables and $E(X\mid Y)=E(X)$, but $X$ and $Y$ are not independent.
101754
Transformation of Random Variable $Y = X^2$
46865
Proof of linearity for expectation given random variables are dependent
75842
Quotient Distribution of Positive Independent Random Variables
122719
Show that random variables $X$ and $Y$ are not independent, but nevertheless Cov$[X,Y] = 0$
156092
Existence of independent and identically distributed random variables.
14930
Prove that the average of iid Gaussian random variables is Gaussian
95928
Independence and orthogonality
129964
Sum of independent Poisson random variables is a Poisson random variable
86729
Are squares of independent random variables independent?
114953
Find $E[N]$ for $N =\min\{n:U_1+U_2\cdots+U_n>1\}$ where $U_1,U_2, . . .$ are independent uniform (0,1) random variables.
118867
Independence of Gaussian variables