Let $X$ and $Y$ be independent Gaussian random variables with means $1$ and $2$ and variances $3$ and $4$ respectively. What is the minimum possible value of $\mathbf{E}\left[(X+Y-t)^{2}\right]$, when $t$ varies over all real numbers?
- $7$
- $5$
- $1.5$
- $3.5$
- $2.5$