In a particular region, earthquakes occur at an average rate of 3 per decade (one decade = 10 years), following a Poisson distribution. Find:
1) the probablity that the fourth earthquake after time t = 0 arrives within 2 years of the third earthquake
2) the probability that the fourth earthquake arrives by time t = 5 years
3) the probability that the elapsed time between the third earthquake to the tenth earthquake exceeds a decade?
4) the expected time and variance until the arrival of the next eight earthquakes
So what I have so far is: Let X be the number of earthquake occurences per decade so X~Poisson(3)
I am unsure of how to continue cause i am having difficulty with this topic. a little help to get me started on these would be greatly appreciated.