$\lambda=\frac{1}{\sqrt{2}} \frac{k T}{\pi \sigma^{2} P}$ and $\lambda=\frac{m}{\sqrt{2} \cdot \pi \sigma^{2} d}$

Here, $\sigma=0$ diameter of molecule and

$k=Boltzmann's\, constant$

$\Rightarrow \lambda \propto 1 / d, \lambda \propto T$ and $\lambda \propto 1 / P$

Hence, mean free path varies inversely as density of the gas. It can easily proved that the mean free path varies directly as the temperature and inversely as the pressure of the gas.