Download Statistics 400 - Lecture 2

Statistics 270 - Lecture 8
• Last day/Today: Discrete probability distributions
• Assignment 3: Chapter 2: 44, 50, 60, 68, 74, 86, 110
Example
•
Bernoulli Distribution:
•
X takes on two possible values:
•
p(x)=px(1-p)1-x
•
This is the probability distribution function or probability mass function
•
p is called a:
•
The collection of all pdf’s for different values of p, for example, is called
Example (Chapter 2 – 11)
•
A garage specializing in engine tune-ups knows that 45% of all tune-ups
are done on 4 cylinder vehicles…40% on 6 cylinder cars and the rest are
eight cylinder cars
• What is the pdf (pmf)?
• What is the probability that a randomily selected car has at least 6
cylinders
• What is the probability that the car has at most 6 cylenders
• Cumulative Distribution Function (cdf): The cdf of a discrete
rv with pmf p(x) is defined, for each x, by
• Properties of the cdf:
Example
• Have 3 flips of a coin
• X=number of heads observed
• p(x)=
• F(x)=
Example
• Plot of cdf
•
Example (Chapter 2 – 13)
•
A mail order company has 6 telephone lines
• Let X denote the number of lines in use at a specific time
• The pmf for X is:
x
p(x)
0
1
2
3
4
5 6
.10 .15 .20 .25 .20 .06 .04
• What is the probability that between 2 and 5 lines (inclusive) are
active?