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?