# STAT 1430 Lecture 21: Binomial Distribution March 19, 2019

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20 Mar 2019
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STAT1430.01Lecture 19Binomial Distribution March 19, 2019
Binomial Distribution
o Type of variable: Discrete
o Used when: Counting times of an event occurs in a sample of n.
o Example: numbers in favor out of n=100
Conditions for a binomial
o You have a series of n observations
o Each observation is independent
o Each observation has only two possible categories:
Success/Failure
Yes/No
o The probability for success equals p, and is the same for each observation
The mean and variance of the binomial
o If X has a binomial distribution with n and p
o Mean of X:
o Variance of X:
o Standard Deviation of X:
Binomial Probability Formula
o X has a binomial distribution
n independent trials
P=probability of success on each trial
X=number of success
o P(x)=
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