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First, disclaimer: that is a question I thought about and not something I found in a book so it might be flawed but I don't think so (someone correct me if I am wrong)

According to the UN, $267$ babies are born each minute while according to another source $120$ people die each minute, since less amount of people are born compared to the amount of people who die, what's the probability that the population decreases after a minute?

What I thought about:

I thought about tackling the problem by representing the birth and death rate by $2$ independent random variable $X,Y$ respectively and finding $P(X-Y<0)$ by I have no experience when it comes to convolution of random variables and I don't know if my idea is reasonable/feasible, any help would be appreciated?

Sergio
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    One problem is that you do not know the distributions of deaths: the possibility of large numbers of simultaneous deaths in natural or man-made disasters will affect the probability (ignoring this will lead to a very small number) – Henry Dec 28 '20 at 12:47
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    As observed, the answer depends on the underlying distributions for births and deaths during a one minute period. If we assume both are independent and both follow Poisson distributions with means 267 (for births) and 120 (for deaths), then the distribution of the difference is a Skellam distribution - see here – WA Don Dec 28 '20 at 14:29
  • and is there any way to find that or will it just be based on assumptions? – Sergio Dec 28 '20 at 17:51
  • I’m voting to close this question because I believe the population is actually decreasing now. – Parcly Taxel Dec 30 '20 at 04:44

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