Final answer:
The mean of the Poisson process with rate λ, independent of a random variable with mean μ, is λμ.
Step-by-step explanation:
The mean of the Poisson process {n(t), t ≥ 0} with rate λ, independent of the nonnegative random variable t with mean μ and variance σ^2 is given by λμ.
To understand this, we need to understand the relationship between the Poisson and exponential distributions. If the time between two successive events follows the exponential distribution with mean μ, and if these times are independent, then the number of events per unit time follows a Poisson distribution with mean λ = 1/μ.
Therefore, the mean number of events per unit time is given by λμ, which is the formula for the mean of the Poisson process.