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**Problem statement:** Suppose that $(X_1,P_1), \ldots, (X_n,P_n)$ are independent random vectors with $X_i|P_i \approx Bernoulli(P_i), P_i \approx beta(\alpha_i,\beta_i)$, for $i = 1,2,\dots, n$. Find $P(X_i=k)$.

Shouldn't $P(X_i=k)$ be $P(X_i=n)$, and shouldn't $\approx$ be ~, and shouldn't $(\alpha_i, \beta_i)$ be $(\alpha,\beta)$?