Please solve the following Bayesian problem with steps, thank you!

Consider the problem of comparing proportions from two binomial distributions, 61 and 02. We observe y1 distributed as Binomial(21, 61) and y2 distributed as Binomial(72, 02). We want to derive the posterior distributions of 01 and 02. Let's consider the case of dependent priors for 61 and 02. That is, knowledge of the value of 6 may influence the prior belief about the location of the second proportion 02. For example, the Australian Technical Advisory Group on Immunisation (ATAGI) has recommended that Pfizer is the preferred vaccine for people aged 60 and under. So what proportion of people under age 60 are willing jump the Pfizer queue and get the alternative AstraZeneca vaccine which is more readily available? Let 0 denote the proportion of people aged 30-39 who are willing to get the AstraZeneca vaccine. Let 02 denote the proportion of people aged 40-49 who are willing to get the AstraZeneca vaccine. Because we are considering adjacent age groups, the vaccine preferences of people in the first age group may affect the vaccine preferences of people in the second age group and vice versa. That is, the belief that 0 is close to say 7% might lead us to believe that the value of 02 is also close to 7%. This belief implies the use of dependent priors for 01 and 02. What are the options for a dependent prior? Howard (1998) proposed a special form of dependent prior between 1 and 02 expressed as follows. First, consider a logit transformation of the parameters Of and 02. That is, define 01 71 = loge] - 01 and 72 = 10ge] - 02 To model the dependency, let 72/71 ~ Normal(mean = 71, stdev = o). Howard (1998) proposed the following general form of the dependent prior p(01, 02) oce-(1/2)u op-1(1 -01)8-105-1(1 -02)6-1 where u = _loge ( 82(1-02) (a) [3 marks] Explain the role of each of the hyperparameters (a, B, k, 6, o) (b) [2 marks] Is the joint prior on p(01, 02) defined above a conjugate prior? Explain why or why not