Power Function

$\mu \mapsto G(\mu ):={\mathbb{P}}_{\mu }\left(\text{ reject }{H}_0\right)\left(\mu \in H_0\cup H_1\right)$ Probability that $H_0$ gets rejected based on some unknown $\mu$.

• $\alpha (\mu )$ is probability of Type 1 Error for $\mu$
• $\beta (\mu )$ is probability of Type 2 Error for $\mu$

Power of the test: $1-\beta (\mu )$