query: Distribution of $X_1X_2+X_3X_4$
positive_passages.docid: 150591
positive_passages.text: Sum of two normal products is Laplace?
negative_passages.docid: 3199
negative_passages.text: Number of positive integral solution of product $x_{1} \cdot x_{2} \cdot x_{3}\cdot x_{4}\cdot x_{5}=1050$ is
negative_passages.docid: 107179
negative_passages.text: Partial fraction expansion of $\frac{1}{x(x+1)(x+2)\cdots(x+n)}$
negative_passages.docid: 108801
negative_passages.text: Given that $xyz=1$, prove that $\frac{x}{1+x^4}+\frac{y}{1+y^4}+\frac{z}{1+z^4}\le \frac{3}{2}$
negative_passages.docid: 30688
negative_passages.text: Prove that $\frac{x_1}{1+x_2+x_3+\ldots+x_n}+\frac{x_2}{1+x_1+x_3+\ldots+x_n}+\ldots+\frac{x_n}{1+x_1+x_2+\ldots+x_{n-1}}\ge\frac{n}{2n-1}$.
negative_passages.docid: 93994
negative_passages.text: Distribution of $\sum_{j=1}^n\ln\left(\frac{X_{(j)}}{X_{(1)}}\right)$ when $X_i$'s are i.i.d Pareto variables
negative_passages.docid: 140650
negative_passages.text: Find the distribution of sum and product of standard normal random variables
negative_passages.docid: 66905
negative_passages.text: Variance of Binomial Distribution $E[X^2]$
negative_passages.docid: 48108
negative_passages.text: (Probability) How many integer solutions are there to the inequality $x_1 + x_2 + x_3 \le 17$
negative_passages.docid: 22586
negative_passages.text: Distribution of $(XY)^Z$ for $(X,Y,Z)$ i.i.d. uniform on $(0,1)$
negative_passages.docid: 146491
negative_passages.text: Number of solutions of $x_1+x_2+\dots+x_k=n$ with $x_i\le r$
negative_passages.docid: 77754
negative_passages.text: Given that $X \sim \operatorname{Binomial}(n,p)$, Find $\mathbb{E}[X(X-1)(X-2)(X-3)]$
negative_passages.docid: 41925
negative_passages.text: What is the distribution of primes modulo $n$?
negative_passages.docid: 42024
negative_passages.text: What is the distribution function of $\left( \begin{smallmatrix} X \\ (-1)^nX \\ \end{smallmatrix}\right)$ where $X\sim N(0,1)$
negative_passages.docid: 1119
negative_passages.text: A normal divided by the $\sqrt{\chi^2(s)/s}$ gives you a t-distribution -- proof
negative_passages.docid: 2877
negative_passages.text: Show $\sum\limits_{n=0}^{\infty}{2n \choose n}x^n=(1-4x)^{-1/2}$
negative_passages.docid: 150908
negative_passages.text: Find the probability function of $X_1+X_2$ in geometric distribution