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?