1. For each of the following, display the likelihood in the form of (8.82) and the conjugate prior in the form of (8.83):

(a) the multivariate normal case with known precision (section 8.2).

(b) the normal linear model (section 8.3) with known precision.

(c) the univariate normal with known mean and unknown precision (section 8.4).

(d) the univariate normal with both mean and precision uncertain (section 8.5).

(e) the normal linear model with uncertain scale (section 8.6).

(f) the multivariate normal distribution with uncertain precision and certain mean (section 8.7.6).

(g) the multivariate normal distribution with both mean and precision matrix uncertain

(section 8.8).

(h) the multinomial distribution (section 8.9) – hint: you might want to start with the binomial distribution.