binomsum - Statistics: binomial distribution and...

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: Statistics: binomial distribution and proportions The binomial distribution • The binomial scenario : the binomial distribution is an appropriate tool in the following circum- stances: 1. There are n “trials”. 2. The trials are independent. 3. On each trial, only two things can happen, “success”and “failure”. 4. The probability of a “success” is the same on each trial. It is usual to call this probability p . 5. We count the total number of “successes”. • The total number of successes that we see in such a scenario is a discrete random variable, X say, that can take any integer value between 0 and n inclusive, e.g. we see no heads, 1 head, ... , all heads. The random variable is said to have a binomial distribution with parameters n,p , abbreviated X ∼ b ( n,p ). • It is easy to show that if X ∼ b ( n,p ) then its probability distribution is P ( X = k ) = n k p k (1- p ) n- k = n ! ( n- k )! k ! p k (1- p ) n- k ,k = 0 , 1 ,...,n. • We can show that the probabilities in this distribution add up to one quite easily. You might remember that the binomial theorem states that, for any two numbers a and b , ( a + b ) n = n X...
View Full Document

This note was uploaded on 05/12/2010 for the course APPLIED ST 2010 taught by Professor Various during the Spring '10 term at Universidad Nacional Agraria La Molina.

Page1 / 2

binomsum - Statistics: binomial distribution and...

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