ground state wavefunction is
$$\psi = \left(\frac{1}{\pi a_0^3}\right)^{1/2} e^{-r/a_0}.$$
Calculate $\langle r \rangle$ and the most probable value of $r$ for the H atom in its ground state. Explain with the aid of a diagram why they differ. The wavefunction is $\psi(r,\theta,\varphi) = |1s\rangle = R_{00}(r) Y_{lm}(\theta,\varphi) = (4\pi)^{-1/2} 2a^{-3/2} \exp(-r/a)$.
