STA104/MTH135: Probability

Homework #7: Expectations

Due: Thursday, Oct 30

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

• Problems (pp. 379ff)
  

  5

  12

  14

  19

  42

  51

• Exercises (pp. 389ff)

  1

• Another Problem
  A company has 700 employees who use cellphones. The phone company allows all 700 to share their minutes. Each person can be put either of two plans:
  • 400 minutes for $32/month
  • 800 minutes for $56/month
  Minutes used beyond the purchased minutes cost $.25/minute. Assume the total number of minutes used in a month is a uniform random variable with lower bound 325000 and upper bound 475000. If the employees are assigned with equal probability to the two plans, what is the expected cost of the monthly phone bill? What selection of plans minimizes the expected cost to the company (how many people should be assigned the 400 minute plan, and how many the 800)? What is that minimum expected cost?
  Extra Credit: What is a better distribution for y and how does that change our answers? (this last part is optional with potential extra credit for VERY good answers)
  

Good Luck!