query: Prove that $S_N = \sum_{i=1}^{N} X_{i}$ is exponentially distributed with parameter $p$
positive_passages.docid: 19148
positive_passages.text: PDF of a sum of exponential random variables
negative_passages.docid: 25546
negative_passages.text: Prove that $\sum_{n=1}^{\infty}\exp\left(-n^{\varepsilon}\right)$ converges.
negative_passages.docid: 94794
negative_passages.text: proof that p-value is uniformly distributed when the null hypothesis is true
negative_passages.docid: 110662
negative_passages.text: Show that $P(\mathbb{N})$ is equivalent to $2^\mathbb{N}$
negative_passages.docid: 41100
negative_passages.text: Density of sum of two independent uniform random variables on $[0,1]$
negative_passages.docid: 35277
negative_passages.text: Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true?
negative_passages.docid: 48792
negative_passages.text: Prove $p_n(x) \rightarrow \sqrt{x}$ uniformly as $n \rightarrow \infty$
negative_passages.docid: 142408
negative_passages.text: How to prove Chebyshev's result: $\sum_{p\leq n} \frac{\log p}{p} \sim\log n $ as $n\to\infty$?
negative_passages.docid: 46431
negative_passages.text: Proof that $\sum\limits_i \frac{(p-1)!}i$ is divisible by $p$
negative_passages.docid: 61963
negative_passages.text: Proving that $\sum\limits_{n=0}^{\infty }\frac{1}{(2n)!!}=\sqrt{e}$
negative_passages.docid: 125723
negative_passages.text: Proof of $Y=F_X(X)$ being uniformly distributed on $[0,1]$ for arbitrary continuous $F_X$
negative_passages.docid: 157898
negative_passages.text: Showing that $\sum_{i=1}^n \frac{1}{i} \geq \log{n}$
negative_passages.docid: 72748
negative_passages.text: Proof that $\sum\limits^{\infty}_{i=0}{iP(X > i)} = \frac12(E(X²)-E(X))$ for $X$ nonnegative and integer valued
negative_passages.docid: 20359
negative_passages.text: Proof of radius of convergence exponential function
negative_passages.docid: 30749
negative_passages.text: The Number of Exponential Summands in a Fixed Interval is Poisson
negative_passages.docid: 14079
negative_passages.text: On the proof that every positive continuous random variable with the memoryless property is exponentially distributed
negative_passages.docid: 82621
negative_passages.text: Show $P\{\xi_1+\dots+\xi_n=1\}=(\sum_{i=1}^n \lambda_i)\Delta + O(\Delta^2)$ (Shiryaev's Probability page 44)