If $P(X=a)=1$ there are only $2^n$ independent non-constant real-valued random variables.
127052
Independence of non-constant real variables
122719
Show that random variables $X$ and $Y$ are not independent, but nevertheless Cov$[X,Y] = 0$
151302
If $X$ and $Y$ are independent random variables, with $Z = \min(X,Y),$ prove that $Z^2\sim\chi^2(1),$
124936
Help with a Probability Proof
110662
Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
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.
77412
Product of $\min$ and $\max$ of $n$ i.i.d. random variables.
65534
Given $P(B\mid A)=1-\varepsilon$ for some $0<\varepsilon<1$ and $P(C\mid B)=1$, prove that $P(C\mid A)≥1-\varepsilon$
98662
$P(|X|\ge\lambda a)\ge (1-\lambda)^2a^2$ for $0\le \lambda \le 1$
31133
Functions of Independent Random Variables
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 $0\leq\lambda\leq 1$.
93634
X,Y,Z independent and $\sim N(1,1)$. Find $P(X+Y \geqq 3Z)$
13831
Find $ P(Z>X+Y)$ where $X,Y,Z \sim U(0,1)$ independently
61758
Limit question on independent random variables (Exercise 4.2.4 from Grimmett and Stirzaker)
3599
show that if ${a_n} \to a$, and $a>0$, then $\exists N$ such that $a_n>0$ for $n \ge N$.
54791
Is it true or false that $\lvert P([0, 1]) \setminus P((0, 1)) \rvert > \lvert P(\mathbb{N}) \rvert$
14664
Sum of indepedent random variables and a constant