Suppose that X1, , Xn form a random sample from a distribution for which the p d f is f(x ), the value of is unknown, and the prior p d f of is () Show that the posterior p d f ( x) is the same regardless of whether it is calculated directly by using Eq (7 2 7) or sequentially by using Eqs (7 2 14), (7 2 15), and (7 2 16)

Question: Suppose that X1, . . . , Xn form a random sample from a distribution for which the p.d.f. is f(x|), the value of

Suppose that X1, . . . , Xn form a random sample from a for which the p.d.f. is f(x|θ), the value of θ is unknown, and the prior p.d.f. of θ is ξ(θ). Show that the posterior p.d.f. ξ(θ|x) is the same regardless of whether it is calculated directly by using Eq. (7.2.7) or sequentially by using Eqs. (7.2.14), (7.2.15), and (7.2.16).

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