Friday, March 1, 2013

Finding the Busier Street

Q: You routinely travel between A & B and have two streets you could drive through to get to B from A. There is a busy street that cuts through both streets so there are signals at X & Y (see fig). You are certain to be stopped at X and Y. Over a period of N days you want to ascertain which of the two routes is a busier one however as you drive you are in no position to count the number of vehicles in front of you and behind you. Assume you have no other data that you can collect other than what you can while driving your car. How do you find the busier street over a period of N days?

Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics)

A: A surprisingly simple solution exists to find this. Take half the journeys \(\frac{N}{2}\) through route AXB and the other half through AYB. Simply keep track of the number of times you are stopped at the signal but are right in front of the queue facing the signal. This is easy to measure and count. In the less busier street you are more likely to be in front of the queue than the busier one!

If you looking to learn probability & algorithms here are some good books.

Introduction to Algorithms
This is a book on algorithms, some of them are probabilistic. But the book is a must have for students, job candidates even full time engineers & data scientists

Introduction to Probability Theory

An Introduction to Probability Theory and Its Applications, Vol. 1, 3rd Edition

The Probability Tutoring Book: An Intuitive Course for Engineers and Scientists (and Everyone Else!)

Introduction to Probability, 2nd Edition

The Mathematics of Poker
Good read. Overall Poker/Blackjack type card games are a good way to get introduced to probability theory

Let There Be Range!: Crushing SSNL/MSNL No-Limit Hold'em Games
Easily the most expensive book out there. So if the item above piques your interest and you want to go pro, go for it.

Quantum Poker
Well written and easy to read mathematics. For the Poker beginner.

Bundle of Algorithms in Java, Third Edition, Parts 1-5: Fundamentals, Data Structures, Sorting, Searching, and Graph Algorithms (3rd Edition) (Pts. 1-5)
An excellent resource (students/engineers/entrepreneurs) if you are looking for some code that you can take and implement directly on the job.

Understanding Probability: Chance Rules in Everyday Life A bit pricy when compared to the first one, but I like the look and feel of the text used. It is simple to read and understand which is vital especially if you are trying to get into the subject

Data Mining: Practical Machine Learning Tools and Techniques, Third Edition (The Morgan Kaufmann Series in Data Management Systems) This one is a must have if you want to learn machine learning. The book is beautifully written and ideal for the engineer/student who doesn't want to get too much into the details of a machine learned approach but wants a working knowledge of it. There are some great examples and test data in the text book too.

Discovering Statistics Using R
This is a good book if you are new to statistics & probability while simultaneously getting started with a programming language. The book supports R and is written in a casual humorous way making it an easy read. Great for beginners. Some of the data on the companion website could be missing.

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