Earthquakes occur in a given region in accordance with a Poisson process with rate 5 per year
a) What is the probability there will be at least two earthquakes in the first half of 2010?
b) Assuming that the event in part(a) occurs , what is the probability that there will be no earthquakes in the first 9 months of 2011?
c) Assuming that a) occurs what is the probability that there will be at least four earthquakes over the first 9 months of 2010?
Through readings I have understood that the inter-arrival times are exponentially distributed, while the distribution of events follow a Poisson Distribution.
For part a) the rate of earthquakes happening in that given region would reduce to (5/2) as we are considering the first half of the year 2010.
As the distribution of earthquakes in this given time frame is Poisson , the probability that the number of earthquakes is greater than or equal to two , would be 1-P[0]-P[1] Where P=[(2.5)^i] *[exp(-2.5)]*[1/(i!)]
For part(b) I think that the rate would be (5/12)*9=3.75 The probability would just be exp(-3.75)
Part (c) is the question I am getting stuck at . Assuming that at least two earthquakes happen in the first 6 months of 2010, how to we find the probability that at least four earthquakes would happen in the first 9 months? Do we have to exploit the memoryless property of exponential distribution here? I am new to Poisson Process and I might be making a conceptual mistake.
a) What is the probability there will be at least two earthquakes in the first half of 2010?
b) Assuming that the event in part(a) occurs , what is the probability that there will be no earthquakes in the first 9 months of 2011?
c) Assuming that a) occurs what is the probability that there will be at least four earthquakes over the first 9 months of 2010?
Through readings I have understood that the inter-arrival times are exponentially distributed, while the distribution of events follow a Poisson Distribution.
For part a) the rate of earthquakes happening in that given region would reduce to (5/2) as we are considering the first half of the year 2010.
As the distribution of earthquakes in this given time frame is Poisson , the probability that the number of earthquakes is greater than or equal to two , would be 1-P[0]-P[1] Where P=[(2.5)^i] *[exp(-2.5)]*[1/(i!)]
For part(b) I think that the rate would be (5/12)*9=3.75 The probability would just be exp(-3.75)
Part (c) is the question I am getting stuck at . Assuming that at least two earthquakes happen in the first 6 months of 2010, how to we find the probability that at least four earthquakes would happen in the first 9 months? Do we have to exploit the memoryless property of exponential distribution here? I am new to Poisson Process and I might be making a conceptual mistake.