1. Chapter 8 The Binomial and Geometric Distributions YMS 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 #

5. Vocab and Simulations Combination Factorial
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 #
HW: , 8.26,

8. The Geometric Distribution
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
HW: p474 #
Review: p479 # , 8.60,