
Julia 1.0 Programming Cookbook
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The Monte Carlo simulation (see the example, http://news.mit.edu/2010/exp-monte-carlo-0517 or https://en.wikipedia.org/wiki/Monte_Carlo_method) is one of the elementary computational techniques. In this recipe, we will explain how it can be implemented efficiently in Julia.
Consider the following problem. Assume that on each day, a random volume of water leaks from a pipe to a container. The amount of water that leaks out is greater than zero, but less than one. How many days do we need to wait till a container having a volume equal to one is filled, if on each day the amount of water that leaks is a uniformly random value between zero and one?
Formally, we repeatedly draw independent random numbers from a uniform distribution on the
interval. How many draws, on average, are required until the sum of drawn numbers is greater than or equal to 1? Let
be a sequence of independent random variables. We want to find the following:
We will approximate...