Solution
= Solution
{c}
Put $z_i=e^{-t_i}-c$. Assume the measurement errors are independent and centered, so $Y_i=\alpha+\beta z_i+\epsilon_i$ with independent $\epsilon_i\sim N(0,\sigma^2)$. Treat the observation times as fixed. The <design matrix> has rows $(1,z_i)$ and parameter vector $(\alpha,\beta)^{\mathsf T}$. Require at least two distinct times so its columns are independent, equivalently $\sum_i z_i^2>0$. This gives the required Gaussian <linear regression model>.