STAT-S 300 Lecture Notes - Lecture 15: Binomial Coefficient, Binomial Distribution, Geometric Distribution
Section 6.3 Notes- Binomial and Geometric Random Variables 10-21-13
• Binomial Settings and Binomial Random Variables
o Binomial setting arises when we perform several independent trials of the same
chance process and record the number of times a particular outcome occurs
▪ 4 conditions
• Binary? The possible outcomes of each trial can be classified as
“success” or “failure”
• Independent? Trials must be independent; knowing the result of
one trial must not have any effect on the result of any other trial
• Number? Number of trials n of the chance process must be fixed
in advance
• Success? On each trial, the probability p of success must be the
same
o Binomial random variable- the count X of successes in a binomial setting
▪ Possible X values are whole numbers from 0 to n
▪ Probability distribution- table or histogram
▪ B(µ, σ)
o Binomial distribution- probability distribution with parameters n and p, where n
is number of trials of the chance process and p is the probability of a success on
any one trial
• Binomial Probabilities
o The number of ways of arranging k successes among n observations is given by
binomial coefficient
for k = 0, 1, 2, …, n where
and
▪ Binomial coefficient
not related to fraction
▪ Calculator
• Type first number
• MATH
• Scroll to PRB
• nCr
• Enter
• Type second number
• Enter
• Enter
o Binomial probability- if X has the binomial distribution with n trials and
probability p of success on each trial, the possible values of X are 0, 1, 2, …, n
▪ If k has any one of these values, then
▪ Calculator
• Distributions (2nd VARS)- ON AP TEST DEFINE N, P, K
• Binompdf (n, p, k) computes P(X = k)
• Binomcdf (n, p, k) computes P(X < k)
• Mean and Standard Deviation of a Binomial Distribution
o If a count X has binomial distribution with number of trials n and probability of
success p, mean and standard deviation are:
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