query: For three variables $X,$ $Y,$ and $Z,$ prove that the sum of all the pairwise correlations is atleast $-3/2$
positive_passages.docid: 9621
positive_passages.text: Bound for the correlation of three random variables
negative_passages.docid: 122944
negative_passages.text: Prove $|y''(x)| \leq 40$ for all $x \in [1,3]$.
negative_passages.docid: 28218
negative_passages.text: Elementary proof for $\sqrt[3]{xyz} \leq \dfrac{x+y+z}{3}$
negative_passages.docid: 45220
negative_passages.text: Proving the sum of two independent Cauchy Random Variables is Cauchy
negative_passages.docid: 139065
negative_passages.text: Proving $\csc\frac\alpha2+\csc\frac\beta2+\csc\frac\gamma2 \ge 6$, where $\alpha$, $\beta$, $\gamma$ are the angles of a triangle
negative_passages.docid: 76347
negative_passages.text: Shorter proof for some equvalences
negative_passages.docid: 83449
negative_passages.text: Proof with 3D vectors
negative_passages.docid: 1258
negative_passages.text: Prove $3^n = \sum_{k=0}^n \binom {n} {k} 2^k$
negative_passages.docid: 50226
negative_passages.text: Prove the identity $\sum_{k=0}^{n}\sum_{r=0}^{k} \binom{k}{r} \binom{n}{k} = 3^n$
negative_passages.docid: 143765
negative_passages.text: To Show that $\exp(tX)\exp(tY)= \exp(t(X+Y)) + (1/2)t^2[X, Y] +o(t^3)$
negative_passages.docid: 49209
negative_passages.text: Prove $(x+y)(y+z)(x+z)≤\frac8{27}(x+y+z)^3$
negative_passages.docid: 154703
negative_passages.text: Use combinatorics to prove $L\left(n,k\right)=\sum_{j=0}^{n}{ n\brack j}{j\brace k}$
negative_passages.docid: 108704
negative_passages.text: Help with proof of $|x+y| \geq |x|-|y|$
negative_passages.docid: 27922
negative_passages.text: prove that $\binom{n}{0}^2+\binom{n}{1}^2+\binom{n}{2}^2+\cdots+\binom{n}{n}^2=\binom{2n}{n}$
negative_passages.docid: 90218
negative_passages.text: Proving $\frac{x}{y} +\frac{y}{z} + \frac{z}{x} \ge 3$ for positive $x,y,z$
negative_passages.docid: 82742
negative_passages.text: Proving that ${x +y+n- 1 \choose n}= \sum_{k=0}^n{x+n-k-1 \choose n-k}{y+k-1 \choose k} $
negative_passages.docid: 14956
negative_passages.text: Sum of 2 Normally Distributed Random Variables With a Correlation