# Density Matrix Characterization

I am working a two dimensional Hilbert space with basis {$|0\rangle, |1\rangle$} and I am trying to show that the density matrix is characterized by 3 real numbers and show that these three numbers are the expected values of the Pauli matrices.

I understand that a density matrix is given by $M_{ij} = \langle i|\rho|j\rangle$ where $|i\rangle$ is an orthonormal basis of $H$ and $\rho$ is the density operator. How do I go about showing this?