1. Section 8.2 Geometric Distributions
AP Statistics
January 15, 2009
CASA

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

8. Better formulas
AP Statistics, Section 8.2.2

9. Exercises
odd
odd
AP Statistics, Section 8.2.2