Section 8.2 Geometric Distributions AP Statistics January 15, 2009 CASA

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

Formulas for Geometric Distribution AP Statistics, Section 8.2.2

AP Statistics, Section 8.2.2

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

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

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) +(1/6)*(5/6)) 1-geometcdf(1/6,2) AP Statistics, Section 8.2.2

Better formulas AP Statistics, Section 8.2.2

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