1. Chapter 6 Binomial and Geometric Random Variables
Binomial vs. Geometric
Chapter 6
Binomial and Geometric
Random Variables

2. Combinations
Formula:
Practice:

3. Developing the Formula
Outcomes
Probability
Rewritten
OcOcOc
OOcOc
OcOOc
OcOcO
OOOc
OOcO
OcOO
OOO

4. Developing the Formula
n = # of observations
p = probablity of success
k = given value of variable
Rewritten

5. BINS BITS Binomial vs. Geometric What is Binomial??? Just check your
The Binomial Setting The Geometric Setting
What is Binomial???
Just check your
BINS
What is Geometric???
Just check your
BITS

6. Binomial vs. Geometric The Binomial Setting The Geometric Setting
Binary: Only two possible
Outcomes (Success/Fail)
1. Binary: Only two possible outcomes (Success/Fail)
Independent: The observations are all independent
2. Independent: The observations are all independent
Number: There is a fixed number of trials
Trials: We go until the first success
Success: The probability of success is the same for each trial
4. Success: The probability of success is the same for each trial

7. Working with probability distributions
State the distribution to be used
Binomial or Geometric
Define the variable
X = number of …
State important numbers
Binomial: n & p
Geometric: p

8. X = # of people use express
Twenty-five percent of the customers entering a grocery store between 5 p.m. and 7 p.m. use an express checkout. Consider five randomly selected customers, and let X denote the number among the five who use the express checkout.
binomial
n = p = .25
X = # of people use express

9. What is the probability that two used express checkout?
binomial
n = p = .25
X = # of people use express

10. What is the probability that at least four used express checkout?
binomial
n = p = .25
X = # of people use express

11. X = # of people who believe…
“Do you believe your children will have a higher standard of living than you have?” This question was asked to a national sample of American adults with children in a Time/CNN poll (1/29,96). Assume that the true percentage of all American adults who believe their children will have a higher standard of living is .60. Let X represent the number who believe their children will have a higher standard of living from a random sample of 8 American adults.
binomial
n = p = .60
X = # of people who believe…

12. Interpret P(X = 3) and find the numerical answer.
binomial
n = p = .60
X = # of people who believe
The probability that 3 of the people from the
random sample of 8 believe their children will
have a higher standard of living.

13. X = # of people who believe
Find the probability that none of the parents believe their children will have a higher standard.
binomial
n = p = .60
X = # of people who believe

14. The Mean and Standard Deviation of a Binomial Random Variable
If X is a binomial random variable with probability of success p on each trial and n number of trials, the expected value and std. dev. of the random variable is

15. Developing the Geometric FormulaX
Probability

16. The Mean of a Geometric Random Variable
If X is a geometric random variable with probability of success p on each trial, the expected value of the random variable (the expected number of trials to get the first success) is

17. X = # of disc drives until defective
Suppose we have data that suggest that 3% of a company’s hard disc drives are defective. You have been asked to determine the probability that the first defective hard drive is the fifth unit tested.
geometric
p = .03
X = # of disc drives until defective

18. X = # of free throws until miss
A basketball player makes 80% of her free throws. We put her on the free throw line and ask her to shoot free throws until she misses one. Let X = the number of free throws the player takes until she misses.
geometric
p = .20
X = # of free throws until miss

19. What is the probability that she will make 5 shots before she misses?
geometric
p = .20
X = # of free throws until miss
What is the probability that she will miss 5 shots before she makes one?
geometric
p = .80
Y = # of free throws until make

20. X = # of free throws until miss
What is the probability that she will make at most 5 shots before she misses?
geometric
p = .20
X = # of free throws until miss