Neural networks may seem mysterious to most people, and thus theirs capabilities are often overestimated. However, in truth, any neural network is just a combination of elementary mathematical operations and in turn, a computational graph. In this post, I am going to show you to how to build a simple neural network with two layers for a classification problem and the math behind it. Part I here is about forward-propagation and the computational graph.

Today we are going to look at Problem 40 from the book 50 Challenging Problems in Probability by Frederick Mosteller. However, instead of solving it analytically, we are going to use the Monte Carlo method (random sampling) to solve it.

The problem goes like this:

Shuffle an ordinary deck of 52 playing cards containing four aces. Then turn up cards from the top until the first ace appears. On the average, how many cards are required to produce the first ace?