Multiple random variable, their expected values, markov chains

Multiple random variable, their expected values, markov chains

I'm reading a paper "Modeling TCP Throughput: A Simple Model and its
Empirical Validation"
In this paper, they modeled TCP throughput using a Markov regenerative
process.
Question 1. There are three probability variables $Y_i$, $\alpha_i$,
$W_i$. Given "$Y_i = \alpha_i + W_i - 1$", they directly used that "$E[Y]
= E[\alpha] + E[W] - 1$". Is it correct? Why is this correct?
Question 2. There is "$W_i = W_{i-1} / 2 + X_i / b$", where $W_i$ is the
Markov chain. Given that, they used that "$E[W] = E[W] / 2 + E[X] / b$"
with assumption that $W_i$ and $X_i$ are independent. I don't know why
this is valid.
Please help me, thank for your help ;)