Statistics 101: Trees

• Administrivia:
  • Exams should be done Friday--see the TAs if you want them before next Wednesday
  • Need to do finance exercise before next class (in groups of 2 or 3 people)
  • Makeup exam: Tonight, 6-8. Room 108-109 Vance Hall

Trees

• Options are valuable
  • Options in walking around town
  • Options on a date
  • Options on making more CD's
  • Options in finance

• Option is the ability to make a choice AFTER more information is collected
• How valuable is an option?
• Abba's example about a product launch.

  4 million profit if successful. 2.5 million loss if not successful.

  P(success) = .6, P(+ test|success) = .8, P(+ test|failure) = .4.

  • E(profits without test) = 4*.6 - 2.5*.4 = 1.4 million
  • E(profits perfect info) = 4*.6 = 2.4 million
  • Value of perfect information = 1 million.
  • E(profits with test) = (draw tree) = .12 Million
  • Value of sample information

• Does it always pay to do a test for a product launch?

  10 million profit if successful. 1 million loss if not successful.

  P(success) = .9, P(+ test|success) = .9, P(+ test|failure) = .1.

  • E(profits without test) = 8.9 million
  • E(profits perfect info) = 10 million
  • Value of perfect information = 1 million.
  • E(profits with test) = (draw tree) = 8.9 Million
  • Value of sample information = 0 million

• Cutting a CD
  • costs $5000 to make 1000 disks
  • costs $7000 to make 2000 disks
  • 2nd printing costs $4000 for the first 1000 disk
  • Sell each disk for $7
  • P(selling 1000) = .9 P(selling 2000) = .1
  • How many should be produced in the first printing?
  • Fixed cost = $10,000.