11-42. Suppose X1, . . . ,Xn is a random sample drawn from a Poisson probability mass function f (x; nλ) = e−nλ (nλ)X X! ,X = 0, 1, 2, . . . ,λ > 0. If Y = ni

=1 Xi ∼ f (x; nλ) and y denotes the sample realization of Y, then it can be shown that a 100(1 − α)% confidence interval for λ is

(1, 2) =  1 2n

χ2 1−(α/2),2y, 1 2n

χ2

α/2,2(y+1)

.

For n = 15 and y = 10, determine a 95% confidence interval for λ.