Dying Population

Consider a population that originally consists of $N$ individuals. Each individual dies independently of one another, and the time of the last death has no bearing on when the next death occurs. When there are exactly $i$ individuals in the population, the rate of death of each individual in the population is $\mu_i$. Find the expected amount of time until the population goes extinct when $N = 4$ and $\mu_i = \frac{1}{5-i}$.