The density function of the absolute speed of a molecule is given by the Maxtell distribution

\[ p(x)=\frac{4 x^{2}}{\alpha^{3} \sqrt{\pi}} e^{-\frac{x^{2}}{\alpha^{2}}} \text { for } x>0 \]

and \(p(x)=0\) for \(x \leqslant 0(\alpha>0\) is a constant). Find the average speed of a molecule, its variance, the mean kinetic energy of the molecule (the mass of the molecule is \(m\)) and the variance of the kinetic energy.