The Narrowest Window for a Third Correlation
Three random variables $X, Y, Z$ satisfy $\operatorname{corr}(X,Y) = 4/5$ and $\operatorname{corr}(Y,Z) = 4/5$. What is the smallest possible value of $\operatorname{corr}(X,Z)$? Give a reduced fraction.
Related problems & prerequisites
Worth solving first
Source: Classic constraint on correlation matrices; no single originator. Statement written for AxiomIQ.