easy Probability
A release-checked easy problem for training Linearity of Expectation, Expected Value/LOTUS.
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 $\mu_i = \frac{1}{5-i}$.
This Probability problem is tagged Linearity of Expectation, Expected Value/LOTUS. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.
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