I'm working with the book "Markov Chains" by J.R.Norris, and I'm stuck on the following passage. Specifically, could someone explain why we have that $$E[X_t | T=s] = 2\mu(t-s)$$ here?
2026-03-25 12:16:26.1774440986
mean population growth of a simple birth process
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At time $T$ the number of individuals grows from 1 to 2. So given $T=s$, the conditional expectation of the number of individuals at time $t$ will be $2\mu(t-s)$, twice the expectation arising from one individual after $t-s$ time units.