Chapter 5 Review MDM 4U

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Chapter 5 ReviewMDM 4U

• Gary Greer

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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?

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5.1 Probability Distributions and Expected Value

• ex what is the expected value for rolling an 8
  sided die?
• ans 1(?) 2(?) 3(?) 4(?) 5(?) 6(?)
  7(?) 8(?) 4.5

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5.2 Pascals Triangle and the Binomial Theorem

• determine the number of paths using Pascals
  Triangle
• use the binomial theorem to expand binomials
• find a particular term in a binomial expansion
• formulas are present on exam

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5.2 Pascals 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)

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5.2 Pascals Triangle and the Binomial Theorem

• ex expand (3 x)³
• ans

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5.2 Pascals Triangle and the Binomial Theorem

• ex find the term in the following with d²

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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?
• (?)(?)(?)(?)

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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

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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

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5.4 Normal Approximation of Binomial Distribution

• calculate s 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

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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

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5.4 Normal Approximation of Binomial Distribution

• ex what is the probability of Mr. Greer getting
  between 15 and 20 sixes?
• ans

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5.5 Simulations

• will not be covered in examination