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5. (10 points) Suppose you have two sensors with known variances v 1 and v 2 , but unknown
(and the same) mean . Suppose we observe n 1 observations from sensor 1 and n 2 observations
from sensor 2. Let D represent the data from both sensors. What is the posterior p ( D ) ,
assuming a non-informative prior for . What are the explicit expressions for the posterior mean
and variance?

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  • 1. 5. (10 points) Suppose you have two sensors with known variances v 1 and v 2 , but unknown (and the same) mean . Suppose we observe n 1 observations from sensor 1 and n 2 observations from sensor 2. Let D represent the data from both sensors. What is the posterior p ( D ) , assuming a non-informative prior for . What are the explicit expressions for the posterior mean and variance?