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Chapter 5 Review MDM 4U

Chapter 5 Review MDM 4U. Gary Greer. 5.1 Probability Distributions and Expected Value. determine the probability distributions for discrete random variables determine the expected value of a discrete random variable

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Chapter 5 Review MDM 4U

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  1. Chapter 5 ReviewMDM 4U Gary Greer

  2. 5.1 Probability Distributions and Expected Value • determine the probability distributions for discrete random variables • determine the expected value of a discrete random variable • ex: what is the probability distribution for results of rolling an 8 sided die?

  3. 5.1 Probability Distributions and Expected Value • ex: what is the expected value for rolling an 8 sided die? • ans: 1(⅛) + 2(⅛) + 3(⅛) + 4(⅛) + 5(⅛) + 6(⅛) + 7(⅛) + 8(⅛) = 4.5

  4. 5.2 Pascal’s Triangle and the Binomial Theorem • determine the number of paths using Pascal’s Triangle • use the binomial theorem to expand binomials • find a particular term in a binomial expansion • formulas are present on exam

  5. 5.2 Pascal’s Triangle and the Binomial Theorem • ex: find the number of paths through a grid where you can only move up or right • ans: C(7,4) or C(7,3)

  6. 5.2 Pascal’s Triangle and the Binomial Theorem • ex: expand (3 + x)³ • ans:

  7. 5.2 Pascal’s Triangle and the Binomial Theorem • ex: find the term in the following with d²

  8. 5.3 Binomial Distributions • recognize a binomial experiment situation • successive events (trials) • same probability • two possible outcomes • calculate probabilities for these situations • ex: roll an 8 sided die 4 times. what is the probability that the first will be a 1 and the rest will be something other than a 1? • (⅛)(⅞)(⅞)(⅞)

  9. 5.3 Binomial Distributions • ex: A family decides to buy 5 dogs. If the chances of picking a male and female are equal, what is the probability of getting 3 males? • ans: using binomial probability distribution formula:

  10. 5.3 Binomial Distributions • calculate the expected value for trying a test 4 times if you have a 60% chance of passing each time • ans: E(x) = np = 4(0.60) = 2.4 • so you are expected to pass 2.4 tests

  11. 5.4 Normal Approximation of Binomial Distribution • calculate σ and the mean, given the number of trials and the probability • determine whether a binomial random variable can be approximated by a normal distribution (p308) • calculate probabilities of data points or ranges of data, given the number of trials and the probability using z-scores

  12. 5.4 Normal Approximation of Binomial Distribution • ex: Mr. Greer tosses a die 100 times. What is the probability of less than 15 sixes? • ans:

  13. 5.4 Normal Approximation of Binomial Distribution • ex: what is the probability of Mr. Greer getting between 15 and 20 sixes? • ans:

  14. 5.5 Simulations • will not be covered in examination

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