Introduction to Probability Models

Lecture 19

Qi Wang, Department of Statistics

Oct 4, 2017

Reminders

  1. The third homework is posted and due on Oct 16
  2. No class on Oct 6 as Exam 1 compensation

Named Random Variables

  • Bernoulli
  • Binomial
  • Hypergeometric
  • Poisson
  • Geometric

Example 1

A college student is running late for his class and does not have time to pack his backpack carefully. He has 12 folders on his desk, 4 include HW assignments due today. He grabs 3 of the folders randomly and when he gets to class, counts the number of them that contain HW.

  1. What is the random variable here? What are the parameters?
  2. What is the expected number of folders with HW in them? What is the variance of X?
  3. What is the probability that 2 folders contain HW?
  4. What is the probability that fewer than 2 folders contain HW?

Time for Quiz

Example 2

Ron is doing his homework for Potions class and has lost his copy of Magical Drafts and Potions. Ron has forgotten whether to add mistletoe berries or juniper berries to his potion. Since Ron is in a hurry, he’s going to randomly pick one of these types of berries. The probability that he adds the mistletoe berries to his potion is 0.643. If he adds the mistletoe, the probability the potion works is 0.92. On the other hand, if he adds the juniper berries, the probability that the potion works is just 0.11

  1. Construct a well-labeled tree diagram for Ron’s potion
  2. What is the probability that Ron added juniper berries and the potion did not work?
  3. What is the probability that the potion worked?
  4. If the potion did not work, what is the probability that Ron added mistletoe berries?
  5. Is whether the potion worked independent of what type of berry Ron added? Answer YES or NO, and show mathematically why or why not.