Measures of Central Tendency: Mean, Median and Mode
Notes Day 6: Bernoulli Trials
1.
2.
3.
4. BERNOULLI TRIALS AND THE BINOMIAL DISTRIBUTION
So far in our discussion of probability we have learned about
combinations and permutations because they help us find the number
of ways a certain event can happen. Using that information we
calculate probabilities. Today we are learning a formula that is used
for very specific situations. We will start with a definition:
A Bernoulli experiment is a random experiment, the outcome of
which can be classified as either a success or failure
(e.g., female or male, life or death, nondefective or defective, heads
or tails, pass or fail).
A sequence of Bernoulli trials occurs when a Bernoulli experiment is
performed several independent times so that the probability of
success, p, remains the same from trial to trial.
If the probability of a success = p, and the probability of a failure = q
then q = 1p because the probability of a success and failure must add
up to 1.
Binomial Distribution
In a sequence of Bernoulli trials we are often interested in the total
number of successes and not in the order of their occurrence. If we let
the random variable X equal the number of observed successes in n
Bernoulli trials, the possible values of X are 0,1,2,…,n. If x success
occur, where x=0,1,2,...,n , then nx failures occur. The number of
ways of selecting x positions for the x successes in the x trials is: nCx
Citation:
http://cnx.org/content/m13123/latest/