First Semester in Numerical Analysis with Julia, 2020a

CHAPTER 1. INTRODUCTION 28
Sometimes we are interested in relative frequency histograms where the height of
each bin is the relative frequency of the numbers in the bin. Adding the option "density=true"
outputs a relative frequency histogram:
In [67]: y = randn(10^5);
hist(y,50,density=true);
Exercise 1.2-1: In Julia you can compute the factorial of a positive integer n by the
built-in function factorial(n). Write your own version of this function, called factorial2,
using a for loop. Use the @time function to compare the execution time of your version and
the built-in version of the factorial function.
Exercise 1.2-2: Write a Julia code to estimate the value of π using the following
procedure: Place a circle of diameter one in the unit square. Generate 10,000 pairs of
random numbers (u, v) from the unit square. Count the number of pairs (u, v) that fall into