statistics question

Number 1of these question is from Bayesian statistical inference  topic. so , please use the formula and define the parameters accordingly. please a detailed solution is needed

Number 2 is from Likelihood Ratio Test. the LRT must be derived according to the instruction. Also, the rejection region must be well defined and C for level α = 0.05. please, ensure they are well defined with few comments. A detailed step by step solution is needed

Solution can be uploaded in handwritten form in order to save time and effort as long as it is clear and readable.

Lastly, time for collection  is 11:00 a.m

Thanks