Your team is evaluating different types of operating systems for various applications in a new technological project involving data processing, user interaction, and real$-$time control. You need to understand how different OS types fit different use cases$\mathrm{.}2\mathrm{.}1$ Define a batch operating system and provide a real$-$world example where it is effectively utilized.$(3$ marks$)2\mathrm{.}2$ Explain the concept of a time$-$sharing operating system and illustrate its application with an example.$(4$ marks$)2\mathrm{.}3$ Describe a distributed operating system and provide an example of its use in a technological setting.$(4$ marks$)2\mathrm{.}4$ Discuss the characteristics of real$-$time operating systems $($RTOS$)$ and give a practical example of where an RTOS is essential.$(4$ marks$)$