10.19 Asme that X,. . . . , X, denotes an i.i.d. sample from N ( O , I), so that

.k I 13 - N(13, l/n). Let Y denote a new observation from the same distribution as the Xs. Adopt a vague prior density for 6, and show that the resulting predictive density for 0,12) is N ( k 1 + l/n).