Piecewise linear probability density on a bounded interval: normalising height and vertex from a given expected value

A continuous random variable \(Y\) takes values between \(0\) and \(4\). Its probability density function \(\mathrm{g}\) is

\(\mathrm{g}(y)=\begin{cases}\dfrac{m}{k}y, & 0\leq y\leq k,\\ \dfrac{m}{k-4}(y-4), & k<y\leq4,\\ 0, & \text{otherwise},\end{cases}\)

where \(k\) and \(m\) are constants with \(0<k<4\) and \(m>0\). The graph of \(\mathrm{g}\) is shown below.

1. Show that \(m=0.5\).[2]

The expected value of \(Y\) is \(2.2\).

2. Find the value of \(k\).[4]