Correlation of a Number with Its Square
Let $X$ be uniform on $[0,1]$. What is the correlation between $X$ and $X^2$? Give an exact closed form (a decimal rounded to 3 or 4 places is also accepted).
Related problems & prerequisites
Worth solving first
- Correlation of Sum and Difference 2.0/10
- Variance of Two Dice 2.0/10
Source: Standard calculation in correlation texts; no single originator. Statement written for AxiomIQ.