Chapter 3 (3.4 - 3.6) 2114

Chapter 3 (3.4 - 3.6) 2114 - Discrete random variables and...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Discrete random variables and probability distributions Chapter 3 (3.4 - 3.6) 1 The Binomial Probability Distribution 2 The Binomial Probability Distribution Consider the following random experiments and random variables: Flip a coin ten times. Let X = number of heads obtained. A worn machine tool produces 1% defective parts. Let X=number of defective parts in the next 25 produced. In the next 20 births at a hospital, let X = the number of female births. 3 The Binomial Probability Distribution The random variable in each case is a count of the number of trials that meet a specified criterion. Each trial can be resulting in either a ‘success’ or ‘failure’. 4 5 Binomial Experiment An experiment for which the following four conditions are satisfied is called a binomial experiment . 1. The experiment consists of a sequence of n trials, where n is fixed in advance of the experiment. 2. The trials are identical, and each trial can result in one of the same two possible outcomes, which are denoted by success ( S ) or failure ( F ). 3. The trials are independent. 4. The probability of success is constant from trial to trial: denoted by p . Given a binomial experiment consisting of n trials, the binomial random variable X associated with this experiment is defined as X = the number of S ’s among n trials. Binomial Experiment 6 The true Binomial experiment requires an infinite or conceptual population or replacement when sampling from a finite population. Suppose each trial of an experiment can result in S or F , but the sampling is without replacement from a finite population of size N…then the experiment is not a true Binomial . However, if the sample size n is at most 5% of the population size, the experiment can be analyzed as though it were exactly a binomial experiment. 7 Binomial Experiment Example: Sam Young is a 71.6% free throw shooter. What is the likelihood that he will make 7 of his next 10 free throws? 8 Probability mass function (pmf) of a Binomial random variable (rv) Because the pmf of a binomial rv X depends on the two parameters n and p , we denote the pmf by b ( x ; n , p ) x n x n x p p C p n x b-- = ) 1 ( ) , ; ( , x = 0,1,2…n otherwise 9 Example: A card is drawn from a standard 52- card deck. If drawing a club is considered a success, find the probability of a. exactly one success in 4 draws (with replacement). b. no successes in 5 draws (with replacement)....
View Full Document

This note was uploaded on 04/17/2011 for the course ENGR 0020 taught by Professor Rajgopal during the Spring '08 term at Pittsburgh.

Page1 / 40

Chapter 3 (3.4 - 3.6) 2114 - Discrete random variables and...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online