b) generate a sample with size n=100 (number of observations) from the population (randomvariable);c) Compute the mean and its 95 percent confidence interval;d) Plot the histogram (the relative frequency) of the sample, and compare it with the proba-bility distribution of the population (random variable) in a);1.2IntroductionSimulation is a way of thinking. It tells stories in a logical way. Just as every story has actors, plots,and contexts, so does simulation. In a story, we want to know how the actors interact, under whatcontext, and what are the outcome of their interactions. In simulation,random variablesare ouractors, and we seek to understand how and why their interplay leads to certain outcomes.For each simulation, we must first specify the relevant random variables. Like actors, they eachhave names and behaviors (personalities, characters). For example, Bernoulli, Binomial, and Nor-mal are the names of typical random variables.Their behaviors are uniquely defined by theirdistribution functions—probability distribution function (PDF)f, or cumulative distribution func-tion (CDF)F. Depending on the problem, either one can be pleasant to work with. Their relationisF(x) =∫x−∞f(t)dtfor continuous case, andF(x) =∑ti≤xf(ti).