Statistics 270 - Lecture 8

1
Statistics 270 - Lecture 8
2

• Last day/Today Discrete probability
  distributions
• Assignment 3 Chapter 2 44, 50, 60, 68, 74, 86,
  110

3
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 pdfs for different values
  of p, for example, is called

4
Example (Chapter 2 11)

• A garage specializing in engine tune-ups knows
  that 45 of all tune-ups are done on 4 cylinder
  vehicles40 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

5

• Cumulative Distribution Function (cdf) The cdf
  of a discrete rv with pmf p(x) is defined, for
  each x, by

6

• Properties of the cdf

7
Example

• Have 3 flips of a coin
• Xnumber of heads observed
• p(x)
• F(x)

8
Example

• Plot of cdf

9

10
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
• What is the probability that between 2 and 5
  lines (inclusive) are active?