The amounts of successive type 1 claims are independent exponential random variables with mean $1000… 1 answer below »

There are two types of claims that are made to an insurance company. Let Ni (t) denote the number of type i claims made by time t , and suppose that {N1(t ), t  width= 0} and {N2(t ), t  width= 0} are independent Poisson processes with rates λ1 = 10 and λ2 = 1. The amounts of successive type 1 claims are independent exponential random variables with mean $1000 whereas the amounts from type 2 claims are independent exponential random variables with mean $5000. A claim for $4000 has just been received; what is the probability it is a type 1 claim?

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