(a) Suppose that you can observe data that are independently and identically distributed as N(μ, 1). Your prior distribution for μ is N(m, v). After observing n₁ data with sample mean ₁, find your posterior distribution for μ. You now observe a second sample of size n2 and with mean 2. Derive your new posterior i. by sequentially using the new data to update the posterior you obtained from the first sample, and ii. by using all the data to update your original prior. Confirm that these two approaches yield the same answer.