STA104/MTH135: Probability

Homework #8: More Expectations

Due: Thursday, Nov 6

Text Problems are from Sheldon Ross, A First Course in Probability (6th edn).

• Problems (pp. 379ff)
  

  40

  70

• Exercises (pp. 389 ff)

  4

  19

  48

  54

• Another Problem
  
• Cary wanders across Duke's campus, giving $1 to strangers (all students). Assuming the students are, independently, equally likely to be freshmen, sophomores, juniors, or seniors, how much money should Cary expect to pay to give a dollar to someone from each class? (HINT: Let X₁ be the number of dollars given until students from at least 1 class have a dollar; X₂ the number of additional dollars given until students from at least 2 classes have dollars; X₃ the number of additional dollars given until students from at least 3 classes have dollars; etc. Obviously E[X₁]=1; what about X₂, X₃, X₄?)
• What's the probability Cary spends no more than $5?

Good Luck!