8/25/2023

Introductions

• Your major
• Your background with probability, mathematics, and statistics
• Something you want us to know about you
• What you did this summer
• Anything else you would like to tell us

Course Roster

Course Web Page

Google Drive Folder - all of your assignments will be submitted electronically to your individual folder

Syllabus

Birthday Problems

Each box of a particular brand of cereal contains one of a set of n different plastic animals.  Suppose that the animal in each box is equally likely to be any one of the set of n, independently of what animals are in other boxes.  What is the expected number of cereal boxes a collector must buy in order to obtain a complete set of animals?

• Let's check your intuition
  • Guess the answer when n=6
  • Guess the answer when n=10
• Simulation can be an extremely powerful tool for these problems - illustrate some R scripts (see My Drive\Math336-Probability-F2023\!Class Material folder for some examples).
  • How would you simulate the answer when n=6?
    
  • How would you simulate the answer when n=10?
• Challenge: think about how you would solve this expected value problem for a general value of n?

Please read Sections 1.1 - 1.6 for class on Monday