University of Michigan
EECS 445
UNIVERSITY OF MICHIGAN Department of Electrical Engineering and Computer Science EECS 445 — Introduction to Machine Learning Winter 2022 Homework 4 REMEMBER to submit your completed assignment to Gradescope by 10:00pm ET on Wednesday, April 13. Your submission can be either handwritten or typed. Assign all pages to their respective questions. Inco
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UNIVERSITY OF MICHIGAN Department of Electrical Engineering and Computer Science EECS 445 — Introduction to Machine Learning Winter 2022 Homework 4 REMEMBER to submit your completed assignment to Gradescope by 10:00pm ET on Wednesday, April 13. Your submission can be either handwritten or typed. Assign all pages to their respective questions. Incorrectly assigned pages will not be graded. 1 Maximum Likelihood Estimate [24 pts] Sanjeev is gearing up for summer vacation and needs to buy some sunscreen this weekend. However, due to time constraints, he can only go to one of the two grocery stores near him: Kroger or Costco. Sanjeev wants to go to a grocery store that has a larger stock of sunscreen. He asks his friends for advice. Over the past several weeks, each of his friends have chosen to visit Kroger with the same probability γ, and Costco with probability 1 − γ. While at the store, they count the number of sunscreen bottles in stock. • The number of sunscreen bottles at Kroger follows a distribution with parameter λ, pK(x|λ) = 2 xλ x e −2λ x! . • The number of sunscreen bottles at Costco follows a distribution with parameter µ, pC(x|µ) = µ x e −µ/2 2 xx! . The following table is his friends’ observation for the past several weeks. Observance i Store z (i) Storage x (i) 1 Kroger 2 2 Kroger 6 3 Costco 4 4 Kroger 5 5 Costco 3 6 Costco 8 7 Kroger 10 8 Costco
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