Bayesian estimation example:

We have two measurements of state (x) using two sensors. x1=3 from sensor 1 and x2=5 from sensor 2. We know that sensor 1 has zero mean Gaussian noise with variance=1 and sensor 2 has zero mean Gaussian noise with variance=0.25. Find MMSE estimate of x and its variance.

Solution: From the code attached we get:

Expected value of x=4.6
Variance of x=0.2

This can be related to Kalman filter estimation as:
K=1/(1+0.25)=0.8
x=3+K*(5-3)=4.6
P=(1-K)*1=0.2