i$.$ Monte Carlo simulation has its origin in physics. However, it has been used in a variety of fields. Explain why Monte Carlo simulation is widely used in finance. Give one example of an application of Monte Carlo simulation in the field of finance.

$[5$ marks$]$

ii$.$ List and discuss the desirable properties of a random number generator.

$[5$ marks$]$

iii. Consider three randomly generated variables $Z_1,Z_2,$ and $Z_3.$ Explain what the following two figures below show.