Combine two distributions to new one & scale parameter modifying probability depending on category

Questions version agnostic
10

Another question:
Is it there a possibility to reweight the combined distribution by the sd? Somthing like

combined = pm.Normal('combined', mu=( (pred_bias*sqrt(var) + y*sigma) / (pred_bias+y)), sigma = np.sqrt(1/ ((1/var) + (1/sigma**2))))