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Section 8.2 Geometric Distributions

Section 8.2 Geometric Distributions. AP Statistics January 6, 2010 Berkley High School. The Geometric Setting. Each observation falls into one of just two categories, which for convenience we call “success” or “failure” You keep trying until get a success

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Section 8.2 Geometric Distributions

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  1. Section 8.2Geometric Distributions AP Statistics January 6, 2010 Berkley High School

  2. The Geometric Setting • Each observation falls into one of just two categories, which for convenience we call “success” or “failure” • You keep trying until get a success • The observations are all independent. • The probability of success, call it p, is the same for each observation. AP Statistics, Section 8.2.2

  3. Formulas for Geometric Distribution AP Statistics, Section 8.2.2

  4. AP Statistics, Section 8.2.2

  5. Calculating Probabilities • The probability of rolling a 6=1/6 • The probability of rolling the first 6 on the first roll: • P(X=1)=1/6. • geometpdf(1/6,1) • The probability of rolling the first 6 after the first roll: • P(X>1)=1-1/6. • 1-geometpdf(1/6,1) AP Statistics, Section 8.2.2

  6. Calculating Probabilities • The probability of rolling a 6=1/6 • The probability of rolling the first 6 on the second roll: • P(X=2)=(1/6)*(5/6). • geometpdf(1/6,2) • The probability of rolling the first 6 on the second roll or before: • P(X<2)=(1/6) +(1/6)*(5/6) • geometcdf(1/6,2) AP Statistics, Section 8.2.2

  7. Calculating Probabilities • The probability of rolling a 6=1/6 • The probability of rolling the first 6 on the second roll: • P(X=2)=(1/6)*(5/6). • geometpdf(1/6,2) • The probability of rolling the first 6 after the second roll: • P(X>2)=1-((1/6) +(5/6)*(1/6)) • 1-geometcdf(1/6,2) AP Statistics, Section 8.2.2

  8. Better formulas AP Statistics, Section 8.2.2

  9. Exercises • 8.37-8.40 • 8.41-8.53 odd • 8.55-8.65 odd AP Statistics, Section 8.2.2

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