Statistics Midterm 2 Information
Chapter 7.2 Binomial Distribution
- Binomial distribution special case of discrete probability distribution.
- The word binomial is derived from bi for “two” and nominal for “numbers”, suggesting a reference to trials (such
as coin fillips) that have only two possible values or numbers that could result.
- A “success” denotes the occurrence of an outcome in which we are interested, such as tossing a head, and a
“failure” denotes obtaining the opposite outcome.
- A binomial distribution can also be called a trial (sometimes called a Bernoulli trial), since a trail is a 2 possible
outcome random experiment of the sort described above.
- Each unique sequence of outcomes for all of the trials combined may define one possible outcome for the
- Binomial experiment an experiment such as the two coin flips, that consists of a sequence of identical and
independent Bernoulli trials.
- Binomial random variable a variable that counts the number of successes (regardless of exact sequence)
among the trial results in the binomial experiment.
These conditions must be met:
1) The experiment consists of n identical trials.
2) There are only two, mutually exclusive, results possible for each trial.
3) All of the trials are independent.
4) The probabilities of success are constant for each trial.
Calculating the probabilities for a binomial random variable:
P(a) = The number of ways A can occur .
the number of different outcomes possible in the sample space.
N = fixed number of trials
x = specific number of success
p = probability of success in one trial
(1 – p) = probability of failure in one trial
P(x) = probability of getting exactly X successes among N trials
Example: Number of
Tails in 2 Tosses of Coin
n = 2; p = 0.5 X P(X)
0 1/4 = .25