W2D3 T3 E1 solution bug

[JesseLivezey]

The solution in T3 contains the following

"""
params (dict): a dictionary of model paramters: (F, Q, H, R, mu_0, sigma_0)
"""
...
# simulate the system
  for t in range(n_timesteps):
    # write the expressions for computing state values given the time step
    if t == 0:
      state[t] = params['mu_0']
    else:
      state[t] = params['F'] @ state[t-1] + zi[t]

which uses a fixed initial state for sampling (the mean) although the parameters imply that you should treat it as a distribution.

We should either provide a static initial state value and correct the solution, or correct the solution to sample from the initial state distribution, such as

if t == 0:
  state[t] = stats.multivariate_normal(mean=params['mu_0'], cov=np.eye(params['sigma_0']).rvs()

[JesseLivezey]

Duplicated in #435