10. Suppose that X1,.., X, form a random sample from the normal distribution with unknown mean u and un- known precision r, and also that the joint prior distribu- tion of u and r is the normal-gamma distribution satisfying the following conditions: E(u) =0, E(t) 2, E(?) = 5, and Pr(e < 1.412) = 0.5. Determine the prior hyperpa- rameters uos do. go, and 8o %3D

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10. Suppose that X, .. , X, form a random sample from
the normal distribution with unknown mean u and un-
known precision r, and also that the joint prior distribu-
tion of u and r is the normal-gamma distribution satisfying
the following conditions: E(u) 0, E(t) 2, E(z) = 5,
and Pr(e <1.412) 0.5. Determine the prior hyperpa-
rameters 4g, hg, ag, and Bo.
Transcribed Image Text:10. Suppose that X, .. , X, form a random sample from the normal distribution with unknown mean u and un- known precision r, and also that the joint prior distribu- tion of u and r is the normal-gamma distribution satisfying the following conditions: E(u) 0, E(t) 2, E(z) = 5, and Pr(e <1.412) 0.5. Determine the prior hyperpa- rameters 4g, hg, ag, and Bo.
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