Solution
= Solution
{c}
Under the physical probability, the stock has mean $\mathbb E S_t=50e^{0.1t}$. Nonnegativity permits interchanging expectation and integration in the accumulated dividends. Hence
$$
\begin{aligned}
\mathbb E X_T&=50e^{0.1T}+0.01\int_0^T50e^{0.1t}e^{0.05(T-t)}\,dt\\
&=50e^{0.1T}+10(e^{0.1T}-e^{0.05T}).
\end{aligned}
$$
Therefore
$$
\boxed{\mathbb E X_T=60e^{0.1T}-10e^{0.05T}\text{ pounds}.}
$$