0
1
2
# of heads
PROB
Binomial Distributions
1. Terms
A binomial distribution is the distribution of a binomial variable.
Binomial variable: {two names} when a variable is measured on a scale with exactly two categories.
Examples: gender, flipping a coin, left hand/right hand,
Probability of A = p(A) = number of outcomes classified as A/total number of possible outcomes
These categories are mutually exclusive: being in one precludes being in another.
2. Context
We generally know the probabilities associated with each of the two categories.
For example: coin toss: p(heads) = .5, p(tails) = .5
But we want to know:
What is the number of times each category occurs in a series of trials (or in a sample of individuals)?
i.e., What is the probability of obtaining 15 heads in 20 coin tosses?
What is the probability of obtaining 20 righthanders in a class of 30 students?
3. Notation
1.
A
&
B
2 categories for the variable (A and B)
2.
p
’s &
q
’s
Probability (or proportion) is identified as:
p: p(A) = probability of A
q: q(B) = probability of B
(p&q are the only possible outcomes) and p + q = 1
3.
n
n
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 Fall '08
 Burns
 Normal Distribution, Poisson Distribution, Standard Deviation, Probability theory, Binomial distribution, Dr. Viji Sathy

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