Solution
= Solution
Both <probability> densities are even, so $\langle x\rangle=0$. The supplied Gaussian moments give $\langle x^2\rangle_0=\sigma^2/2$ and $\langle x^2\rangle_1=3\sigma^2/2$. Therefore $\boxed{\Delta x_0=\sigma/\sqrt2,\quad\Delta x_1=\sqrt{3/2}\sigma}$. The original plots mark these two symmetric rms intervals around the common mean.