Statistics 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)=p x (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: What is the probability that between 2 and 5 lines (inclusive) are active?