Answer: $1 + 0.5t$

The mean function of $Y_t$ is calculated as follows: $\mu_Y(t) = E(Y_t) = E(1 + 0.5t + Z_t)$ Since $1 + 0.5t$ is deterministic (non-random), and $Z_t \sim WN(0,1)$ where $WN$ stands for White Noise with mean 0 and variance 1: $\mu_Y(t) = 1 + 0.5t + E(Z_t)$ Given that $E(Z_t) = 0$: $\mu_Y(t) = 1 + 0.5t$ Therefore, the correct answer is C: $1 + 0.5t$.

Author: Nikitesh Somanthe