Statistics problem, please have detailed steps.

Let (Ya, r;) (i = 1, ...,n) be independent following a linear regression model without intercept, Yi ~ N(Br;, 1), or equavelently Y = Br; te;, where e; ~ N(0, 1) where r1, ..., In are known design constants. (a) (4 points) Write the likelihood function L(B) (b) (8 points) Suppose we use N(0, 1) as the prior distribution for B. Find the posterior distribution of B given observations (91 , 21), . .. . (yn, In). Hint: The prior is a conjugate prior so the posterior distribution is also a Normal distri- bution. This is a distribution of B so treat all given (yi, r;) as constants and you can ignore all multiplicative constants. You just need to find the mean and variance of the posterior distribution]