Am crying but on the inside — you li’l fucker
why don’t you shut up
Life is long and full of terrors
So be a man and buck up
Ashris
Poetry wasn’t working. My earphones were broken and so I had to face the shrieks and wails of the little infants. It’s not like I didn’t empathize — I thought maybe it was the pressure difference or something. That wasn’t the case. When I carefully analysed the behavior of an infant seated three seats across, I was amazed. He started crying as soon as the mother took away the phone from him and paused when he had it back. I stopped empathizing with the shrewd manipulative creature and the rest like him.
I pondered why was it happening over and over again. Irrespective of whether I fly to Boston or to Kochi, there was always some weakling wailing and shrieking. I decided to apply my geeky statistical skills and come up with a formula to predict the probability that my flight will be ruined — so that I am mentally prepared.
The question I wanted to answer was this — given an airport, what is the probability that some baby will cry?
So I flunked my probability and stats course back in college and thus I was wary of doing any fancy poisson curve shizz. I wanted to assume the easiest conditions for me to come with a rough model.
Assumptions : (a) All babies are identical and have equal probability of crying during the flight, (b) The crying of a baby is independent of other babies crying — this is a wrong assumption I admit because the fuckers do get encouraged by seeing other babies crying.
Let’s say the probability that a single baby cries during the flight is p.
If there are n babies, what is the probability that my flight is ruined? By my flight being ruined, I mean that atleast one cries.
Probability of flight ruining = 1-probability(no baby cries)
Probability a baby does not cry = 1-p
Probability no baby cries = (1-p)(1-p)….(1-p) n times = (1-p)^n
So probability that my flight is ruined = 1-(1-p)^n
Let’s verify. If there are 0 babies, I get answer as 0 — makes sense.
If I have 1 baby, the probability is p — okay so this makes sense.
Let’s now try to express n and p as some expression with known variables.
n is easy — its the number of babies. Let’s say n = 𝚿 * N where N is the number of seats in plane and 𝚿 is the fraction of babies — the Babbiette factor, if you wish.
From my observation, in Boston flights, there were about 2 kids while in Kochi flight there were 3. Assuming N=100 for both cases, 𝚿 for Boston was 0.02 and for Kochi was 0.03. Babbiette factor basically suggests what fraction of the people in the flight are infants. How would we model this term? maybe it depends on things like the fertility rate of a city* (higher the fr higher the 𝚿, the GDP of a city — generally higher the GDP, lower the babies and so lower the 𝚿)
*fertility rate = A representative figure for how many babies does a city/state have.
Now, fertility rate is kinda related to GDP (inverse relation), so lets just use one variable. There weren’t any sources online for age distribution of flight passengers, so I decided to assume that. I estimate that in a compartment with 100 seats, the number of babies seated would be 2 for Boston, 3 for Kerala, 4 for Delhi and 6 for Patna. Linearly regresing with the fertility rates (1.54 for Massachusetts, 1.8 for Kerala, 2.4 for Delhi and 3.2 for Bihar), the relation we get is
𝚿 = 0.023*fr-0.0138
Okay, now we have expressed n in terms of fr.
n = N * 𝚿 where 𝚿 = 0.023*fr-0.0138
I am tempted to do the same with p. Let’s do some batshit crazy assumptions. The higher the fr -> higher the population and congestion-> the more the babies cry
I dunno if that’s like some offensive argument but well, I think it makes sense in my head so I will go along unless someone reading this can do a better job.
Let’s say Boston kids are 40% likely to cry, 45% for Kerala kids, 50% for Delhi kids and 60% for Bihar kids.
Again regressing,
p = 0.23+0.114*fr
The final formula for probability comes out to be
1-(1-p)^n where n = N * (0.023*fr-0.0138) and p = 0.23+0.114*fr
Assuming N=100, the graph we get on plotting this is something like this :
If we discard the fertility rate because of the obvious weird assumptions I made, and just assume p=0.5 (Schrodinger baby), here is the probability of flight ruining vs number of babies on plane.
With this knowledge, I was able to distract myself away from the crying. Look at those graphs!
I let the result sink in. Basically no matter what, I was more or less likely going to experience a crying baby on a flying plane. Ugh.
By the time I recovered, the babies fell asleep and they didn’t look that horrible. They were actually cute.
Okay, I don’t have any concluding lines. So, bye.
