This blog post will serve as a quick tutorial to basic probability and random variables, and encoding them in Racket. It assumes basic knowledge with sets and programming.
Continue reading “Encoding probability and random variables in Racket”Category: Mathematics
Stay Home
I would like to mathematically demonstrate how important it is to stay home in times like these. My article will be a very short version of the cite below. Let’s start with a simple task:
Begin by asking how a rumor might spread among a population. Suppose on Day 1 a single person tells someone else a rumor, and suppose that on every subsequent day, each person who knows the rumor tells exactly one other person the rumor. Have students ponder, discuss and answer questions like: “How many days until 50 people have heard the rumor? 100 people? The whole school? The whole country?Exponential Outbreaks: The Mathematics of Epidemics
Formalization of Boolean algebra pt. 2
In my previous post I’ve said that to prove that from 
Introduction and formalization of Boolean algebra
Recently I’ve been teaching my friend boolean algebra for their exams at university. Some exercises included simplifying boolean expressions. While teaching them, I noticed that we mostly relied on the transformation rules and almost mechanically simplified expressions (M of MIU, remember? :))
In this post, we will formalize this algebra and prove some properties about it.
Continue reading “Introduction and formalization of Boolean algebra”
Wisdom of the crowd exercise
According to Wikipedia, the wisdom of the crowd is the collective opinion of a group of individuals rather than that of a single expert. An explanation for this phenomenon is that there is idiosyncratic noise associated with each individual judgment, and taking the average over a large number of responses will go some way toward canceling the effect of this noise.
We’ll take the results of a YouTube video as an example, to test the wisdom of the crowd. I used Majk’s Show as a dataset. It’s a young local guy that interviews random people on the streets, asking them random questions.
We will agree that any hits above 50% will validate the wisdom of the crowd. Follows a table with results:
| Question | Answer | Correct answers (%) | Valid? |
| How do you pronounce “schedule” | sheh·jool or skeh·jool | 13/34 = 38.23% | No |
| Who’s the man on the picture | Albert Einstein | 14/32 = 43.75% | No |
| 8/2(2+2)=? | 16 | 11/25 = 44% | No |
| What’s closer, America or the Moon? | America | 9/22 = 40.9% | No |
| Who was the first president of Macedonia? | Kiro Gligorov | 22/50 = 44% | No |
| What is larger: -4 or -10? | -4 | 20/36 = 55.55% | Yes |
We can further categorize the questions and see where the wisdom of the crowd fails specifically. For example, English seems to be below 40% while everything else is above 40%.
In any case, I think I might have set a bit high grading point for the citizens of my country 🙂 But at least they seem to know how to compare two numbers!
