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Statistics 400
Lecture 10
Section 3.3, 3.4
Expected value and Bernoulli Trials
Review:
Bernoulli Experiment:
A Bernoulli experiment is a random experiment, the outcome of which can
be classified as success and failure.
Let X be random variable of
Bernoulli distribution
.
Outcome
Success
1
Failure
0
Probability
p
q=1p
Notation:
X ~ Ber (p)
Expected value E[X]=p
Variance
Var[X]=pq
A sequence of Bernoulli Trials:
A sequence of Bernoulli experiments are conducted independently and the
probability of success (p) remains the same.
Example:
For a million of instant lottery tickets, suppose that 20% are
winners, If 5 tickets are purchased,
(1) what is the probability we have (0,1,0,1,0)?
Ping Ma
Lecture 10
Fall 2005
 1 
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View Full Document(2) what is the probability we have (0,0,1,1,0)?
(3) What is the probability we have two winning tickets?
Binomial distribution
1. A Bernoulli experiment is performed n times
2. The trials are independent
3. The probability of success on each trial is a constant p; The
probability of failure on each trial is a constant 1p
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 Fall '05
 TBA
 Statistics, Bernoulli

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