## Suppose that a statistical model is given by the family of Bernoulli($\theta$) distributions where $θ \in \Omega = [0, 1]$. Calculate $\psi(\theta)$

Suppose that a statistical model is given by the family of Bernoulli($$\theta$$) distributions where $$θ \in \Omega = [0, 1]$$. If our interest is in making inferences about the probability that two independent observations from this model are the same, then determine $$ψ(θ)$$.

SOLUTION: We have that $$\psi(\theta) = (1-\theta)^2 + \theta^2$$. How?