9.13 A Normal Distribution: You are given a dataset of 3 numbers, -1, 0, 20. You wish to model this dataset with a r distribution with unknown mean μ and standard deviation 1. You will make an MAP estimate of u. The prior on µ is n with mean 0 and standard deviation 10. (a) What is the MAP estimate of μ? (b) A new datapoint, with value 1, arrives. What is the new MAP estimate of µ?

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**9.13 A Normal Distribution:** You are given a dataset of 3 numbers, \(-1, 0, 20\). You wish to model this dataset with a normal distribution with unknown mean \(\mu\) and standard deviation 1. You will make an MAP estimate of \(\mu\). The prior on \(\mu\) is normal, with mean 0 and standard deviation 10.

(a) What is the MAP estimate of \(\mu\)?

(b) A new datapoint, with value 1, arrives. What is the new MAP estimate of \(\mu\)?
Transcribed Image Text:**9.13 A Normal Distribution:** You are given a dataset of 3 numbers, \(-1, 0, 20\). You wish to model this dataset with a normal distribution with unknown mean \(\mu\) and standard deviation 1. You will make an MAP estimate of \(\mu\). The prior on \(\mu\) is normal, with mean 0 and standard deviation 10. (a) What is the MAP estimate of \(\mu\)? (b) A new datapoint, with value 1, arrives. What is the new MAP estimate of \(\mu\)?
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