Page 151 - Statistics for Dummies

Chapter 8: Random Variables and the Binomial Distribution

The variance is in square units, so it can’t be easily interpreted. You use stan-
dard deviation for interpretation because it is in the original units of X. The
standard deviation can be roughly interpreted as the average distance away
from the mean.
Identifying a Binomial
The most well-known and loved discrete random variable is the binomial.
Binomial means two names and is associated with situations involving two
outcomes; for example yes/no, or success/failure (hitting a red light or not,
developing a side effect or not). This section focuses on the binomial random
variable — when you can use it, finding probabilities for it, and finding its
mean and variance.
A random variable is binomial (that is, it has a binomial distribution) if the
following four conditions are met: 135
1. There are a fixed number of trials (n).
2. Each trial has two possible outcomes: success or failure.
3. The probability of success (call it p) is the same for each trial.
4. The trials are independent, meaning the outcome of one trial doesn’t
influence that of any other.
Let X equal the total number of successes in n trials; if all four conditions are
met, X has a binomial distribution with probability of success (on each trial)
equal to p.
The lowercase p here stands for the probability of getting a success on one
single (individual) trial. It’s not the same as p(x), which means the probabil-
ity of getting x successes in n trials.
Checking binomial conditions step by step

You flip a fair coin 10 times and count the number of heads (X). Does X have
a binomial distribution? You can check by reviewing your responses to the
questions and statements in the list that follows:

1. Are there a fixed number of trials?
You’re flipping the coin 10 times, which is a fixed number. Condition 1 is
met, and n = 10.

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