Statistics
Bennie Waller
wallerbd@longwood.edu
434-395-2046
Longwood University
201 High Street
Farmville, VA 23901
Bennie D Waller, Longwood University
Discrete Probability
Bennie Waller
wallerbd@longwood.edu
434-395-2046
Longwood University
201 High Street
Farmville, VA 23901
Bennie D Waller, Longwood University
Discrete Probability Distributions
CHARACTERISTICS OF A PROBABILITY DISTRIBUTION
1.The probability of a particular outcome is between
0 and 1 inclusive.
2. The outcomes are mutually exclusive events.
3. The list is exhaustive. So the sum of the probabilities
of the various events is equal to 1.
DISCRETE RANDOM VARIABLE - A variable that can assume only
certain clearly separated values and is the typically the result of counting
something.
CONTINUOUS RANDOM VARIABLE – A variable that can assume an infinite
number of values within a given range. It is usually the result of some type of
measurement
Bennie D Waller, Longwood University
Probability Distributions
PROBABILITY DISTRIBUTION A listing of all the outcomes of an
experiment and the probability associated with each outcome.
Experiment:
Toss a coin three times.
Observe the number of
heads. The possible
results are: Zero heads,
One head,
Two heads, and
Three heads.
What is the probability
distribution for the
number of heads?
Bennie D Waller, Longwood University
6-4
Discrete Probability Distribution
Mean
X
P(x)
.05
.20
.06
.20
.07
.20
.08
.20
.09
.20
Bennie D Waller, Longwood University
Discrete Probability Distribution
Variance
X
P(x)
.05
.20
.06
.20
.07
.20
.08
.20
.09
.20
Bennie D Waller, Longwood University
Discrete Probability Distribution
Binomial Probability Distribution
• A Widely occurring discrete probability distribution
• Characteristics of a Binomial Probability Distribution
1. There are only two possible outcomes on a
particular trial of an experiment.
2. The outcomes are mutually exclusive,
3. The random variable is the result of counts.
4. Each trial is independent of any other trial
Bennie D Waller, Longwood University
6-7
Binomial Distribution
Bennie D Waller, Longwood University
Binomial Distribution
Probability Distribution of Number of Heads
Observed in 3 Tosses of a Coin
Bennie D Waller, Longwood University
6-9
Binomial Distribution
Calculating means and variances of a binominal distribution
Bennie D Waller, Longwood University
Poisson Distribution
Poisson Probability Distribution
• The Poisson probability distribution is characterized by the
number of times an event happens during some interval or
continuum.
Examples include:
• The number of misspelled words per page in a newspaper.
• The number of calls per hour received by Dyson Vacuum
Cleaner Company.
• The number of vehicles sold per day at Hyatt Buick GMC in
Durham, North Carolina.
• The number of goals scored in a college soccer game.
Bennie D Waller, Longwood University
6-11
Poisson Distribution
Bennie D Waller, Longwood University
Poisson Distribution
Assume baggage is rarely lost by Northwest Airlines.
Suppose a random sample of 1,000 flights shows a total of
300 bags were lost. Thus, the arithmetic mean number of
lost bags per flight is 0.3 (300/1,000). If the number of
lost bags per flight follows a Poisson distribution with u =
0.3, find the probability of not losing any bags.
Bennie D Waller, Longwood University
6-13
Binomial Distribution
Binomial – Shapes for Varying n ( constant)
Bennie D Waller, Longwood University
6-14
Poisson Distribution
Bennie D Waller, Longwood University
6-15
Discrete Probability Distributions
Problem: The arrival of customers at a service desk follows a Poisson distribution. If they
arrive at a rate of two every five minutes, what is the probability that no customers arrive
in a five-minute period?
Bennie D Waller, Longwood University
Example
Problem: Elly's hot dog emporium is famous for its chilidogs. Elly's latest sales indicate
that 30% of the customers order their chilidogs with hot peppers. Suppose 18 customers
are selected at random. What is the probability that exactly ten customers will ask for hot
peppers?
Bennie D Waller, Longwood University
Example
Problem: For the following probability distribution, what is the variance?
Bennie D Waller, Longwood University
Example
Problem: There are eight flights from Minneapolis to St. Cloud each day. The probability
that any one flight is late is 0.10. Using the binomial probability formula, what is the
probability that 1 or more are late?
Bennie D Waller, Longwood University
Example
Problem: There are eight flights from Minneapolis to St. Cloud each day. The probability
that any one flight is late is 0.10. Using the binomial probability formula, what is the
probability that none are late?
Bennie D Waller, Longwood University
End
Bennie D Waller, Longwood University