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Integration is only meaningful for continuous functions. If we are to represent probabilities per day, then wouldn't we have a discrete function, and be obliged to use summation?
You are right if we assume that probability the sun explodes on a day is a constant say
0<p<1, and that the events from each day to day are independent . This would follow a geometric distribution and the probability of the sun explodes on
day k would be [(1-p)^(k-1)]*p.
And to calculate the probability the sun had not exploded for say n days would be
sum of (1-p)^i , i=1,2,3...n, which would be [1-(1=p)^(n-1)]/p .
It is interesting to note however that when we deal with a set of integers that has many elements(such as prime numbers for which there are infinitely many) ,
you can can link them to continuous processes like integration.
One example of this is the Poisson distribution, which is helpful when you want to know how many times an event occurred in a finite period of time.
I imagine that we need to narrow down the time period we want to know if the sun will explode in that time period. for i imagine the probability of the sun exploding within the next few billion years is zero.
20 Apr 2014, 7:41 pm
