Calculation of expectation and variance of a CRV

The continuous random variable \(X\) has probability density function

\[\mathrm{f}(x) = \begin{cases} 4k & , \quad \frac{2}{3} \leq x < 2 \\ kx(4-x) & , \quad 2 \leq x \leq 4 \\ 0 & , \quad \text{otherwise} \end{cases}\] where \(k\) is a constant.

1. Find the value of the constant \(k\).
2. Find \(\mathrm{E}(X)\).
3. Find \(\mathrm{E}(X^2)\).
4. Find \(\mathrm{Var}(X)\) and the standard deviation of \(X\).