I was given the births in a country follow a Poisson process in which on average number of babies born in $24$ hours is $11.7$.
I figured out this indicates $0.4875$ babies are born per hour.
So how can I find the probability of more than $3$ hours between births?
Is this a change in rate? I'm new to probability and statistics.
The answer is $0.2317$, but how was it calculated ?
Best Answer
As per your information, births occur according to Poisson Process with rate parameter $\lambda=0.4875$.
In a Poisson process, the inter occurrence times follow Exponential distribution. We require the probability of the event: the time elapsed between two successive births is more than 3 hours.
This means that we require probability of having no births in an interval of length 3 hours. From Poisson Process this probability is $e^{-\lambda t }=e^{-0.4875 \times 3}= 0.2316564.$