We use Gaussian distribution N(, ²) to track the location of an object in 1-dimensional space. We assume the prior position follows N(4, 9). Then there is a motion, which follows N(2, 6). Then we have a sensor measurement, which follows N(1, 5). Then there is another motion, which follows N(3, 4). What Gaussian distribution does the posterior position follow after each motion and sensing sequentially?

1. [2 points] After the 1st motion:
2. [4 points] After the 1st sensing:
3. [2 points] After the 2nd motion: