Lecture9_print - MA/STAT416 Probability Lecture Notes...

Info iconThis preview shows pages 1–2. 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
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA/STAT416: Probability Lecture Notes Spring 2011 1 Chapter 6: Standard Discrete Distributions March 8, 2011 6 Binomial, Geometric, and Uniform Distributions 6.1 The Binomial Distribution Suppose a coin has probability of heads equals to p (not necessarily 1 2 ) is tossed n times. The coin is not a fair coin. Describe the distribution of X = number of heads. This is the binomial distribution with parameters n and p . X has B ( n,p ). P ( X = x ) = n x p x (1- p ) n- x , x = 0 , 1 , 2 , ··· ,n. Theorem 1. If X has B ( n,p ) , then μ X = E ( X ) = np and var ( X ) = p np (1- p ) . Example 2 . A fair coin is tossed 5 times. Let X denote the number of heads obtained. Describe the distribution. Find the expected value and variance of X . Example 3 . A multiple choice examination has 25 questions, each having 5 choices. The passing grade is 10. Suppose a student, completely unprepared, chooses his answers randomly. What is his probability of passing? What is the most likely number of correct answers he gets? Example 4 . An insurance agent has 15 policy holders that are considered high-risk. Any one of them has a 2.5% probability of making a claim. Letone of them has a 2....
View Full Document

This note was uploaded on 04/23/2011 for the course STAT 416 taught by Professor Staff during the Spring '08 term at Purdue.

Page1 / 2

Lecture9_print - MA/STAT416 Probability Lecture Notes...

This preview shows document pages 1 - 2. Sign up to view the full document.

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