Prove that for any random discrete variable and its median
25605
Why does the median minimize $E(|X-c|)$?
46760
To show that $P(|X-Y| \leq 2) \leq 3P(|X-Y| \leq 1)$
14664
Sum of indepedent random variables and a constant
35956
Proof that a sum of Bernoulli rvs has Binomial distribution
111075
Deriving of formula for finding the length of median
81363
How to compute $P(X>Y)$ if $X$ and $Y$ are independent and exponentially distributed
98733
Proof for the calculation of mean in negative binomial distribution
154706
Spacings between discrete uniform random variables
125723
Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
112392
Can we prove the law of total probability for continuous distributions?
106816
Medians of a triangle and similar triangle properties
54461
Showing independence of random variables
139877
Square of a uniform random variable
143732
Prove random variable $Y_0$ and $\sigma$-algebra $\mathscr{R}$ are independent.
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 $0\leq\lambda\leq 1$.
142325
Two independent geometric random variables - proof of sum
11629
Can a discrete variable take on multiple values, and thus truth values, simultaneously in the mathematical proof below or elsewhere?