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Curiosity On Rails

Scientific explorations of a young enthusiast

void test();

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- March 22, 2017

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Probability and it's probability!

- March 22, 2019

This post seeks to find a free meeting room in my office floor. The shores of Dirac Sea has an interesting puzzle about probabilities which also inspired the results of my findings. Let us say that someone gives you a lopsided bet. Say that with probability \(r\) one gets heads, and with probability \(1 - r\) one gets tails, and you have to pick heads or tails. You only know the outcome of the first event. Let's say after the first toss it came out heads. What is the probability that \(r > 1/2\)? The question seems redundant, the outcome of a bet is determined by another event's probability, basically what we are dealing with is - the probability, of a probability ! One day when going to one of the meeting rooms in my office floor for our daily meeting, none of the meeting rooms were vacant, since this had happened a number of times before as well I thought how would I know if any of the meeting rooms is empty or not. It immediately made me wonder how I could calcul...

Hypothesis to die for, an unbiased die?

- February 04, 2018

Is it possible that the dice (singular form: die) that we get with our monopoly game/other games is not within the rules of it being called an unbiased die ? Maybe not. Hypothesis : Die is unbiased To test this hypothesis, the first question that arises (due to sheer lassitude) is - what will be the minimum number of tests/throws to get enough data of statistical importance? According to Pearson's \(\chi^2\) test , the rule of thumb is to atleast have 5 times the total sample space of a single die. The die has 6 sides, so we need atleast 30 tests . To get more significant results, this will be repeated 3 times to give better results. In the first test, we threw the die 40 times and its values are: 6,4,3,1,2,5,3,1,4,2,5,3,1,1,3,2,5,3,1,2,3,5,4,2,3,6,1,4,2,3,4,2,5,6,2,3,1,2,6,4 : \(sum=127\) Throw methodology: All throws were made with the right hand pivoted at a point and arc length of the throw was marked such that the same distance was covere...

The noise inside your head

- January 19, 2021

Have you ever felt that your head was full and you couldn't think more? To my surprise, that was not just a metaphor, it was quite literally true! For an ever-growing, learning brain, and to keep in-taking information, there is a big price humans have to pay! Not delving into the biology of our brain, I'll try explaining things in a computer scientist friendly way; every-time our brain intakes new information/data, we make stronger synapses (connections) between nerve cells. The strength of these synapses determines how easily we can retrieve information from our brain, and consequently, some synapses become stronger/larger when we repeatedly intake the same information (thus when we want to memorize something, we find revision helpful for later retrieval.) In a single waking day, synapses continuously strengthen/enlarge as we absorb all kinds of experiences, but this process can't happen indefinitely as synapses reach a saturation point - hence 'our head becomes...