Meteorologists model the volume of rain water collected over a given time interval, as a realisation of a compound stochastic process in which the arrival of raindrops is modelled as a realisation of a Poisson process with the size of the raindrops modelled as distributed according to a Gamma distribution. The actuary observed her friend model the rainfall data in a given geographical location, over a 10 minute period, with the data at hand parametrised by an arrival rate of λ = 1 per second and individual raindrop sizes have mean diameter of 2 mm, with a standard deviation of 0.2 mm. The container in which the rain water is being collected however has a leak, from which water escapes at a uniform rate of 1 mm per second. At the beginning of the 10 minute time interval, there is 1 mm of rain water inside the container. Find probability that the contain will be empty over 10min period?
Initially i calculated, arrivals~Po(1/60) in terms of minutes, size~G(100,50). I know for arrivals, i know I have to use the aspect of T1, T2-T1, ... but I'm really dont know where togo?