4.10: (a) If the probability density of X is given by f(x)={ (1)/(xln 3) for 1

Question: Problem 4.10: (a) If the probability density of $X$ is given by

\[f(x)=\left\{ \begin{aligned} & \frac{1}{x\ln 3}\text{ for 1}<x<3 \\ & \text{ }0\text{ elsewhere} \\ \end{aligned} \right.\]

find $E(X)$, $E({{X}^{2}})$ and $E({{X}^{3}})$.