Another poisson distribution question

[romeo6]

Ok,

If the mean time between a single random event occurring is 6 months then is the most probably month for the third event to occur the 18th month?

Thanks!

 

[EnumaElish]

I don't know the answer but here's how I'd go about it. You need to calculate the probability density function (p.d.f.) of the third event occurring within a given time frame. Start from the basics, e.g. the corresponding cumulative distribution function (c.d.f.) will be Prob{third event < t} = Prob{event "one" < t and event "two" < t and event "three" < t} = Prob{event "one" < t} Prob{event "two" < t} Prob{event "three" < t}. Once you calculate the c.d.f., you can then figure out the p.d.f. The expected value of that p.d.f. is your answer.