Suppose we have a stationary object sitting at the origin of our coordinate plane. It then experiences a push in the x-direction and a push in the y-direction. The resulting -displacement follows X ~ N(0, σ^2) and the resulting y-displacement follows Y ~ N(0, σ^2), i.e. both are zero-
mean Gaussian with the same (unknown) variance. Our goal is to estimate that variance.
We have collected data for 5 trials of the absolute distance of the object from the center.
The values are: (2, 3, 1, 1, 2}. What is the maximum likelihood estimate of σ^2?