Section 5.3: Binomial Random Variables
Many problems in probability involve
independently
repeating a random experiment and
observing at each repetition whether a specified event occurs. We label the occurrence of
the specified event a
success
and the nonoccurrence of the specified event a
failure
.
Bernoulli Trials:
A success could be a female child, a head from a coin flip, a 5 on a die, a defective part, a
black in roulette, etc.
A
success
can take on a positive or negative connotation in the context of the example; it
is merely the event we are interested in. Each repetition of the random experiment is
called a trial, and collectively, all the trials are called
Bernoulli Trials
.
We denote
p
as the probability of a
success
on 1 trial.
p
remains constant from trial to
trial.
Conditions for Bernoulli:
1)
the trials are independent of one another
2)
the result of each trial is classified as a success or failure, depending on whether
or not a specified event occurs, respectively
3)
the success probability and therefore the failure probability remains the same
from trial to trial
Note: If we sample from a population 1 at a time, it is Bernoulli if we sample with
replacement but IT IS NOT BERNOULLI if we sample without replacement!
Human Examples: Success= if the person is in school, if they have a college degree, if
they have a job, if they have brown hair, etc.
Sometimes the Bernoulli Distribution is called an indicator function, i.e. it lets one know
whether or not a specific event has occurred.
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 Spring '08
 MARTIN
 Bernoulli, Binomial, Probability, Probability theory, Binomial distribution, 8K, 8  k, 10 90 k

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