From distribution to interval. (a) (pi sim beta_{(43,96)}). Find (I_{0.1}^{pi}), both by exact calculation of (beta), and

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From distribution to interval.

(a) \(\pi \sim \beta_{(43,96)}\). Find \(I_{0.1}^{\pi}\), both by exact calculation of \(\beta\), and by using Normal approximation.

(b) \(\pi \sim \beta_{(7,128)}\). Find \(I_{0.001}^{\pi}\), both by exact calculation of \(\beta\), and by using Normal approximation.

(c) \(\pi \sim \beta_{(2,2)}\). Find \(I_{0.05}^{\pi}\).

(d) \(\pi \sim \beta_{(1,1)}\). Find \(I_{0.12}^{\pi}\) (hint: sketch the graph).

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