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BINOMIAL PROBABILITY DISTRIBUTION A binomial experiment is an experiment that meets the following four conditions: 1. The experiment consists of a sequence of n smaller experiments called trials, where n is fixed in advance of the experiment. 2. Each trial is a Bernoulli trial. In particular, each trial can result in one of the same two possible outcomes, which we generically denote by success (S) and failure (F). 3. The trials are independent, so that the outcome on any particular trial does not influence the outcome on any other trial. 4. The probability of success P(S) is constant from trial to trial; we denote this probability by p. The binomial random variable X associated with a binomial experiment consisting of n trials is defined as X = the number of S's among the n trials. Because the pmf of a binomial rv X depends on the two parameters n and p, we denote the pmf by b(x; n, p). 2. Let n = 4. In the following table, list all the possible outcomes for a binomial experiment with 4 trials, the value x of the rv X for each outcome, and the probability of the observed outcome. Outcome x Probability Outcome x Probability SSSS 4 p^4 FSSS 3 p³(1 - p) SSSF 3 p³(1 - p)

          BINOMIAL PROBABILITY DISTRIBUTION
A binomial experiment is an experiment that meets the following four conditions:
1. The experiment consists of a sequence of n smaller experiments called trials,
where n is fixed in advance of the experiment.
2. Each trial is a Bernoulli trial. In particular, each trial can result in one of the
same two possible outcomes, which we generically denote by success (S) and
failure (F).
3. The trials are independent, so that the outcome on any particular trial does not
influence the outcome on any other trial.
4. The probability of success P(S) is constant from trial to trial; we denote this
probability by p.
The binomial random variable X associated with a binomial experiment consisting
of n trials is defined as
X = the number of S's among the n trials.
Because the pmf of a binomial rv X depends on the two parameters n and p, we
denote the pmf by b(x; n, p).
2. Let n = 4. In the following table, list all the possible outcomes for
a binomial experiment with 4 trials, the value x of the rv X for each outcome, and
the probability of the observed outcome.
Outcome x Probability Outcome x Probability
SSSS 4 p^4 FSSS 3 p³(1 - p)
SSSF 3 p³(1 - p)

BINOMIAL PROBABILITY DISTRIBUTION
A binomial experiment is an experiment that meets the following four conditions:
1. The experiment consists of a sequence of n smaller experiments called trials,
where n is fixed in advance of the experiment.
2. Each trial is a Bernoulli trial. In particular, each trial can result in one of the
same two possible outcomes, which we generically denote by success (S) and
failure (F).
3. The trials are independent, so that the outcome on any particular trial does not
influence the outcome on any other trial.
4. The probability of success P(S) is constant from trial to trial; we denote this
probability by p.
The binomial random variable X associated with a binomial experiment consisting
of n trials is defined as
X = the number of S's among the n trials.
Because the pmf of a binomial rv X depends on the two parameters n and p, we
denote the pmf by b(x; n, p).
2. Let n = 4. In the following table, list all the possible outcomes for
a binomial experiment with 4 trials, the value x of the rv X for each outcome, and
the probability of the observed outcome.
Outcome x Probability Outcome x Probability
SSSS 4 p^4 FSSS 3 p³(1 - p)
SSSF 3 p³(1 - p)

Added by Jason J.

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