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Binomial Distribution (Dr. Monticino)

Binomial Distribution (Dr. Monticino). Assignment Sheet. Read Chapter 15 Assignment # 9 (Due March 30 th ) Chapter 15 Exercise Set A: 1-6 Review exercises: 1,2,3,4 (important),5,6,7,10,11 Re-do example problems in last two lectures

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Binomial Distribution (Dr. Monticino)

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  1. BinomialDistribution(Dr. Monticino)

  2. Assignment Sheet • Read Chapter 15 • Assignment # 9 (Due March 30th) • Chapter 15 • Exercise Set A: 1-6 • Review exercises: 1,2,3,4 (important),5,6,7,10,11 • Re-do example problems in last two lectures • Exam 2 is projected to be on April 11th or 13th depending on when we finish Chapter 18

  3. Overview • Binomial Model • Assumptions • Calculating Probabilities • Examples • Law of Averages

  4. Binomial Model • The binomial distribution is used as a model for a process which is repeated n times. • Each time the process is repeated, outcomes are classified as either successes or failures • Each time the process is repeated there is the same probability of a success occurring • Successive outcomes are independent of one another

  5. Binomial Distribution • Under the assumptions of the binomial model, the probability of k successes out of n repetitions is

  6. Examples • Flip a fair coin 10 times • What is the probability that 10 heads come up? • What is the probability that exactly 8 tails occur? • What is the probability that at least 8 tails occur?

  7. Examples • Roll two fair die 5 times • What is the probability that 5 “doubles” are rolled? • What is the probability that doubles are rolled at most twice • What is the probability that the sum of the die is seven on 3 out of the 5 rolls

  8. Examples • The likelihood of a women developing breast cancer during her lifetime is 1 in 9 • Suppose 8 women are randomly chosen from the population • What is the probability that they all develop breast cancer • What is the probability that at least two will develop breast cancer?

  9. Law of Averages • The law of averages says that if a chance process is repeated a large number of times , then the percentage of times that a particular event occurs is likely to be close to the probability of that event • Provided the assumptions assumed for the binomial model hold • There is always chance error (Dr. Monticino)

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