Question 1:

The digital cameras on an online marketplace have on average 50 reviews and an average rating of 4.30 (out of 5.0). A new digital camera has a rating of 5.0 after getting 2 reviews. Calculate the Bayesian average for this camera?

Question 2:

You are working as a defense attorney and you got a call from your English Professor at the University of Texas that he has been charged for one of the greatest art heist in decades that took place at the Getty Museum in California. Beyond some circumstantial evidence, such as your professor's social media posts revealing her admiration for the paintings stolen, no strong alibi etc., there is only one forensic evidence that can tie the defender to the crime. There was a single fingerprint found at the crime scene and the prosecutor presented evidence that the fingerprint was ran through a huge FBI fingerprint database that includes US criminal prints, civil background check prints and TSA prints, and a single match came back, that of your Professor! This database has approximately 80,000,000 prints. The prosecutor claims that ''There is absolutely no chance of getting such a good of a print match simply by accident''. Even though you are convinced that your professor did not commit this crime, it seems to she is in trouble (or so does the prosecutor think). How can you help her using data science proposal framework (assuming she was not nasty in college) ?

Question 3:

Using the information below, calculate for each book its average rating. Also, calculate for each book its Bayesian average rating. How does the average and Bayesian average rating differ based on the number of reviews for each book. (30 points)