1 / 9

Understanding Geometric Distributions: AP Statistics Guide

This guide delves into the principles of geometric distributions as covered in AP Statistics. Each observation can either be a "success" or "failure," and trials continue until the first success is achieved. We explore key formulas for calculating probabilities, such as the chance of rolling a 6, and how to determine the probability of achieving the first success on various trials. Included are practical exercises to reinforce learning. Perfect for AP Statistics students seeking clarity on geometric settings and probability calculations.

laquinta
Télécharger la présentation

Understanding Geometric Distributions: AP Statistics Guide

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related