Show that $(X_1 \mid X_1 + X_2 + \dots + X_k)$ has binomial distribution, where $X_i$ has Poisson distribution $\lambda_i$
3346
Proof that Conditional of Poisson distribution is Binomial
54905
A classical inequality involving the central binomial coefficient
106699
Symmetric alpha stable distributions with $X_1+X_2+\cdots+X_n \stackrel{d}{=} n^{1/\alpha}X$ as definition
15666
explanation for a combinatorial identity involving the binomial coefficient
19571
Combinatorial proof for $\sum_{k = 0}^n \binom {r+k} k = \binom {r + n + 1} n$
23603
Joint distribution of $X+Y$ and $\frac{X}{X+Y}$
108690
The weighted sum of two independent Poisson random variables
64319
Deriving the canonical link for a binomial distribution
142994
How to show $\sum_{i=1}^{n} \binom{i}{2}=\binom{n+1}{3}$?
92569
Showing that ${\rm E}[X]=\sum_{k=0}^\infty P(X>k)$ for a discrete random variable
148732
Conditional Distribution of Poisson Variables, given $\sum X_i$
93994
Distribution of $\sum_{j=1}^n\ln\left(\frac{X_{(j)}}{X_{(1)}}\right)$ when $X_i$'s are i.i.d Pareto variables
105145
Show that $\mathbb{E}\left(\bar{X}_{n}\mid X_{(1)},X_{(n)}\right) = \frac{X_{(1)}+X_{(n)}}{2}$
16434
Finding the distribution of $5X_{1}^2+2X_{1}X_{2}+X_{2}^2$
158508
Combinatorial Proof for Binomial Identity: $\sum_{k = 0}^n \binom{k}{p} = \binom{n+1}{p+1}$
52557
Derivation of binomial coefficient in binomial theorem.
25148
Deriving the bivariate Poisson distribution