Chap05 Discrete Probability Distribution
Business Statistics
Chapter 5
Some Important Discrete
Probability Distributions
5-1
Chapter Goals
After completing this chapter, you should be able to: Interpret the mean and standard deviation for a discrete probability distribution
Explain covariance and its application in finance
Use the binomial probability distribution to find probabilities Describe when to apply the binomial distribution
Use Poisson discrete probability distributions to find probabilities
5-2
Definitions
Random Variables
A random variable represents a possible numerical value from an uncertain event.
Discrete random variables produce outcomes that come from a counting process (e.g. number of courses you are taking this semester).
Continuous random variables produce outcomes that come from a measurement (e.g. your annual salary, or your weight).
5-3
Definitions
Random Variables
Random
Variables
Ch. 5
Discrete
Random Variable
Continuous
Random Variable
Ch. 6
5-4
Discrete Random Variables
Can only assume a countable number of values
Examples:
Roll a die twice
Let X be the number of times 4 comes up
(then X could be 0, 1, or 2 times)
Toss a coin 5 times.
Let X be the number of heads
(then X = 0, 1, 2, 3, 4, or 5)
5-5
Probability Distribution for a
Discrete Random Variable
A probability distribution (or probability mass function )(pdf) for a discrete random variable is a mutually exclusive listing of all possible numerical outcomes for that random variable such that a particular probability of occurrence is associated with each outcome.
Number of Classes
Taken
Probability
2
0.2
3
0.4
4
0.24
5
0.16
5-6
Discrete Probability Distribution
Experiment: Toss 2 Coins.
T
T
H
H
T
H
T
H
Probability Distribution
X Value
Probability
0
1/4 = .25
1
2/4 = .50
2
1/4 = .25
Probability
4 possible outcomes
Let X = # heads.
.50
.25
0
1
2
X
5-7
Discrete Random Variable
Summary Measures
Expected Value (or mean) of a discrete distribution (Weighted
Chapter 5
Some Important Discrete
Probability Distributions
5-1
Chapter Goals
After completing this chapter, you should be able to: Interpret the mean and standard deviation for a discrete probability distribution
Explain covariance and its application in finance
Use the binomial probability distribution to find probabilities Describe when to apply the binomial distribution
Use Poisson discrete probability distributions to find probabilities
5-2
Definitions
Random Variables
A random variable represents a possible numerical value from an uncertain event.
Discrete random variables produce outcomes that come from a counting process (e.g. number of courses you are taking this semester).
Continuous random variables produce outcomes that come from a measurement (e.g. your annual salary, or your weight).
5-3
Definitions
Random Variables
Random
Variables
Ch. 5
Discrete
Random Variable
Continuous
Random Variable
Ch. 6
5-4
Discrete Random Variables
Can only assume a countable number of values
Examples:
Roll a die twice
Let X be the number of times 4 comes up
(then X could be 0, 1, or 2 times)
Toss a coin 5 times.
Let X be the number of heads
(then X = 0, 1, 2, 3, 4, or 5)
5-5
Probability Distribution for a
Discrete Random Variable
A probability distribution (or probability mass function )(pdf) for a discrete random variable is a mutually exclusive listing of all possible numerical outcomes for that random variable such that a particular probability of occurrence is associated with each outcome.
Number of Classes
Taken
Probability
2
0.2
3
0.4
4
0.24
5
0.16
5-6
Discrete Probability Distribution
Experiment: Toss 2 Coins.
T
T
H
H
T
H
T
H
Probability Distribution
X Value
Probability
0
1/4 = .25
1
2/4 = .50
2
1/4 = .25
Probability
4 possible outcomes
Let X = # heads.
.50
.25
0
1
2
X
5-7
Discrete Random Variable
Summary Measures
Expected Value (or mean) of a discrete distribution (Weighted