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Let X be a random variable with a p.d.f. f_θ in an exponential family {P_θ : θ ∈ Θ} and let A be a Borel set. Show that the distribution of X truncated on A (i.e., the conditional distribution of X given X ∈ A) has a p.d.f. f_θIA/P_θ(A) that is in an exponential family.

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