text: Q:
  
  If I know the parameters of a probability distribution, do I also know the underlying probability measure?
  
  If I have a probability model $(\Omega, \mathcal{F, P})$ with an associated probability distribution, e.g. $Normal(\mu, \sigma)$, and, the parameters $\mu, \sigma$ are known, is the probability measure also known?
  
  A:
  
  Of course not.
  The probability distribution $\operatorname{Normal}(\mu, \sigma)$ is a measure
  $$\mathbb{B}(\mathbb{R}) \to [0,1]$$
  This depends in no way on the probability measure $\mathbb{P}$ of the probability space $(\Omega, \mathcal{F}, \mathbb{P}).$
  
  