1 / 11

Chapter 8 The Binomial and Geometric Distributions YMS 8.1

Chapter 8 The Binomial and Geometric Distributions YMS 8.1. The Binomial Distributions. Binomial Distribution. Distribution of the count X of successes in the binomial setting with parameters n and p

brenna-english
Download Presentation

Chapter 8 The Binomial and Geometric Distributions YMS 8.1

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. Chapter 8The Binomial and Geometric DistributionsYMS 8.1 The Binomial Distributions

  2. Binomial Distribution • Distribution of the count X of successes in the binomial setting with parameters n and p • n is the number of observations and p is the probability of a success on any one observation • The possible values of X are the whole numbers from 0 to n • Denoted by B(n,p).

  3. Binomial Setting • Each observation falls into one of just two categories, “success” or “failure” • There is a fixed number n of observations • The n observations are all independent • The probability of success, p, is the same for each observation

  4. Binomial Calculations • pdf • probability distribution function which assigns value to single outcome X • cdf • cumulative distribution function which assigns value to range of X • Be careful of calculator entries when finding greater than or at least! p445 #8.4-8.8

  5. Vocab and Simulations • Combination • order doesn’t matter • n choose k • Factorial • n! = n x (n-1) x (n-2) x 3 x 2 x 1 and 0! = 1 • Use randbin(1, p, n) to give 1 p% of the time and 0 (1-p)% of the time

  6. Using Binomials • Binomial Probability • where the coefficient is a combination • Binomial Mean & Standard Deviation

  7. Normal approximation to binomial distributions • As the number of trials n gets larger, the binomial distribution gets close to a normal distribution • Rule of thumb • N(np, ) can be used when n and p satisfy np≥ 10 and n(1 – p) ≥ 10 p454 #8.16-8.19 HW: 8.12-8.14, 8.26, 8.32-8.36

  8. YMS 8.2 The Geometric Distribution

  9. Geometric Setting • Each observation falls into one of just two categories: “success” or “failure” • The probability of success, p, is the same for each observation • The n observations are all independent • The variable of interest is the number of trials required to obtain the first success

  10. Calculating geometric probabilities • probability that the first success occurs on the nth trial is • probability that it takes more than n trials to see the first success is

  11. Geometric Mean & Standard Deviation 8.37 and 8.40 HW: p474 #8.44-8.46 Review: p479 #8.55-8.56, 8.60, 8.62-8.63

More Related