Wednesday, January 9, 2013

Bernoulli Trial

Ref : Design for Six Sigma Statistics (

A Bernoulli Trial is a simple experiement with following characteristic :
  1. Each Bernoulli trial has only two outcome :
    • Yes / No
    • Pass / Fail
  2. In an experiment with multi Bernoulli trials, the probability of each of the outcomes is the same in every trial
  3. In an experiment with multiple Bernoulli trials, all trials are mutually independent.
Suppose :
  • p = probability of selecting a defective part
  • n = part are selected from a infinite population
What is the probability of selecting exactly x defective parts ?

This situation has 'n' Bernaoulli trial with a constand probability of selecting a defect 'p'. Since the trials are indenpendent, the joint probabilities are products of individual probabilities.

Each possible sample with 'x' defective parts and (n-x) nondefective parts has a probability of

Also there arecombination of samples of size 'n'with 'x' defects.
Therefore, the probability that a 'n' sample size from a population with a constand probability fo defects 'p' with have exactly 'x' defects is

This probability model is known as Binomial Distribution

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