[Book] False Positives and Positive Fallacies

Conditional Probability

We learned earlier that more details can lead to more restriction and reduce the corresponding probability. More specifically, the probability of event A is always greater than the probability of events A and B.

But details do not always reduce the probability. It can increase the probability by shrinking the sample space. We can be more sure that a specific outcome will occur if we can cross off some of the sample space. This is known as “Bayes’ Theorem”.

Probability, Ratio, and the Law of Large Numbers

Probability and Ratio

You probably know about probability and ratio. Suppose I put 70 of black balls and 30 of white balls in an urn. General statements would be

• The Ratio of black balls (when comparing to all the balls in the urn) is 7:10
• If I draw a ball from the urn, the Probability that I would draw a black ball would be 7 in 10

A new blogspot test message no. 5 on Sept. 18

Gods and Expectation

Blaise Pascal

Blaise Pascal is known as the person who invented the Pascal's Triangle, whose elements are the number of ways to arrange N objects in M places.

But, the story that drew my interest is that he is also the inventor of expectation. And, even more interesting is how he came up with the concept of expectation. Here we go....

Update on NS 2.35 Installation: Command not Found

During the last week, I have got few email about my previous NS2 installation.

The Error Message

After the installation some one type "ns" and get the following error
>>nsbash: ns: command not found
This could be because you have not set the $PATH variable. Therefore, the OS does not know where to look for the command "ns".

The Birthday Problem

Given that everyone’s birthday is absolutely random, how many people
must be in the room such that there is more than even chance (at least
50%) that

• Another person would have the same birthday as you (ANS: 365/2 =
  183 persons)
• Two persons would have the same birthday (ANS: 23 persons)

The difference is that you fix the date in the former. But you let the date vary in the latter. It is obvious that you would need less people in the latter than in the former. But the surprising result is that it is a lot less.

C++ and OTcl Linkage: Result — Passing Values between C++ and OTcl domains

ote: The content in this series is extracted from the book, Introduction to Network Simulator NS2. You may have to read chapter 3 of the book for better understanding.

Introduction
This post is the second post in the series on C++ and OTcl Linkage:

   1. Why Two Languages?
   2. Binding C++ and OTcl classes [Main steps, The mechanism].
   3. Variable binding
   4. OTcl command: Invoking C++ statements from the OTcl domain [ Getting Started, Invocation process, Binding OTcl and C++ ]
   5. Eval: Invoking OTcl statements from the C++ domain
   6. Result: Passing Values between C++ and OTcl domains
   7. Object binding and object construction process.
In the previous post, I blogged about an approach to invoke OTcl statements from the C++ domain using function evalc(...) and evalf(...). This post discusses the way to pass results between C++ and OTcl domains using function result(...).

Passing Values Between C++ and OTcl

View more presentations from Teerawat Issariyakul.
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T. Issaraiyakul and E. Hossain, “Introduction to Network Simulator NS2”, Springer 2009.


You may also find lecture notes and other resource at the following website: http://www.ece.ubc.ca/~teerawat/NS2.htm

Sample Space and Gambling

The Dawn of Sample Sapce

Gerolamo Cardano was an physician, a gambler, and a mathematician. Early in his career, he discovered the concept of sample space, and tried to publish the concept in a book named “The book on Games of Chance”. The manuscript was rejected.

He did not try to published it again. Instead, he used the concept to make a fortune out of gambling. The book was published after his death in 1663. Here is the quote from the book.

“The possible outcomes of a random process can be thought of as a point in the space.”

This space of all possible outcomes is later known to as “sample space”.