Binomial Distribution

1
Binomial Distribution

• A binomial experiment possesses the following
  properties
• 1 a fixed number, n, of trials
• 2 two outcomes for each trial
• 3 constant probability of success on each
  trial
• 4 independence between any two trials

2
Binomial Random Variable

• A discrete random variable that counts the number
  of successes on n trials of a binomial experiment
  is said to be a binomial random variable.

3
Examples of binomial random variables

• The number of spark plugs that fail when a car
  engine is ignited
• The number of heads in twenty tosses of a fair
  coin
• The number of sevens in three rolls of a pair
  of dice
• The number of defective items in a quality sample
  of 25

4
Binomial Mass Function

• x PXx
• 0 p0(1-p)n
• 1 np1(1-p)n-1
• .
• .
• .
• n pn(1-p)0

5
Plots of binomial probabilities
6
Plots n20
7
Plots n 100
8
Expected value and variance of a binomial random
variable

• EB np
• VB np(1-p)