I've been looking into studies of marriage rates in interesting circumstances. I was originally hoping to investigate the coming Chinese marriage experiment, which has just begun as a result of the law set almost three decades ago which only allowed a single child to each household. In the end, I found a study about French marriage rates following WWI, and another about marriage rates immediately following the aforementioned law's ratification.
There were a few mathematical terms I had never heard of, including the Poisson Distribution that I'm currently geeking out over. What a nifty little statistical device! And I think I'm completely failing to apply it properly.
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Ok, the Poisson-distribution is a pretty nice tool to calculate propabilities. All you need is an event that is either true or false and the propability for this event to be true should be low.
For example:
In a climbing gym are 4% people climbing but didn't take the top-rope-test before.
There are 120 climbers in the gym. We want to know the propability that there are 7 climbers without top-rope tag among these 120 ppl.
To be precisely you would have to calculate like this:
P(X=7)=0.04^7*0.96^113*120!/7!/113!
(P(X=7) means the propability for 7 ppl without tag among our 120; 0.04^7*0.96^113 is the propability for the case you lined them all up and the first 7 have no tag and the last 113 have a tag - won't be likeliy; 120!= 120*119*118*...*1; and 120!/7!/113! is the number of combinations, on what position the 7 no-tag-guys could stand in your line)
That makes P(X=7)=0.0967=9.67%
That's the EXACT probability for 7 no-tag guys out of 120. If you had 1000000000 ppl, you wouldn't be able to calculate that.
And therefore you have the Poisson-distribution, with which you can calculate a good approximation of that propability.
Poisson: P(k)=lambda^k*e^(-lambda)/k!
That lambda is the expected number of occurrences. In our case its
lambda=0.04*120=4.8 no-tag guys expected
k=7
e=2.718... Euler Number
Here we go:
P(k=7)=4.8^7*2.718^(-4.8)/7!=0.0959=9.59%
That's pretty close to 9,67%!
Hope that was helpful!
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