You are given the posterior for the Bernoulli parameter \(\pi\), and numbers \(m, s, k\), and \(l\). Find the predictive distributions for \(K_{+m}\) and \(L_{+s}\), and calculate the probabilities \(P\left(K_{+m} \leq kight)\) and \(P\left(L_{+s}

(a) Posterior: \(a_{1}=19, b_{1}=31 . m=5, s=5, k=3, l=7\).

(b) Posterior: \(a_{1}=5, b_{1}=96 . m=20, s=4, k=3, l=12\).

(c) Posterior: \(a_{1}=42, b_{1}=13 . m=7, s=14, k=4, l=5\).

(d) Posterior: \(a_{1}=434.5, b_{1}=177.5 . m=32, s=20, k=23, l=8\).