Thorne Wolfenbarger - Blog

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math

A collection of 4 issues

Placing Marbles Into Buckets - Expected Max Marbles

This question is inspired by an estimation problem I noticed in the workplace. We wanted to predict the QPS our service needs to support when client requests are rare but come in bursts when they do arrive. Problem Statement We have N marbles and M buckets. Randomly and uniformly distribute

Pricing Options with the Black-Scholes Model [Short]

Recently, I have been learning about optimal options pricing under various sets of assumptions. The introduction to risk-neutral options pricing is the Black-Scholes model, which assumes you have an arbitrage free market with at least one risk-free asset and one risky asset. Additionally you assume that the log-price of the

Unconventional Statistics With Dice – Expected Minimum Roll from 3 dice

In a previous post I discussed the potential benefits for using Monte Carlo simulations in place of traditional statistical modeling. Here, I would like to consider an interesting stats puzzle that I found to be non-trivial (read hard), which has a relatively tidy solution. First, we will investigate the solution

Monte Carlo Simulations: For When Math Is Just Too Hard

“Monte Carlo simulations are used to model the probability of different outcomes in a process that cannot easily be predicted due to the intervention of random variables.“ (Investopedia, 2019) For me, ease of prediction is completely relative. If doing the math on a process proves itself too cumbersome or boring,