The binomial distribution (‘coin-flipping’ model): X is the number of successes in n independent trials (success or failure), p is the fixed probability of success.
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Description
A
Short Overview
1.
The binomial distribution (‘coin-flipping’
model): X is the number of successes in n
independent trials (success or failure), p is the fixed probability of success. This is the ‘yes/no sampling
with replacement from a finite
population’ function. The binomial model also gives good approximations when
sampling without replacement, as
long as the sample size is very small compared to the population size.
So ‘true (1)
and false (0)’ are answers to the question “Cumulative?”
2. The Poisson distribution (‘number of occurrences per unit of measure’
model):
Assumes the units (minutes, hours,
miles, acres, etc.) are independent. Assumes that the mean number of
occurrences per unit is known.
3. The Hypergeometric distribution (‘number of successes in sample’
model):
x is the
number of ‘successes’ (or just
occurrences of some characteristic) in a sample of size n randomly selected
from a ‘population’ size N containing M successes (or occurrences of the
characteristic). This is the ‘yes/no sampling without replacement from a finite population’ function. If the sample size is small compared to the
population size, the binomial distribution gives a good approximation to the
hypergeometric.
4. The Insert Tab can be used to make
a histogram of these probability models if a probability table is computed
first. For example if X is binomial with n = 10 and p = .75,
the probability distribution and
histogram are as given on the next page.
