™ Random
variable
a variable (typically represented by x) that has
a single numerical value, determined by
chance, for each outcome of a procedure
™ Probability distribution
a description that gives the probability for each
value of the random variable; often expressed
in the format of a graph, table, or formula
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
™ Discrete
™
random variable
either a finite number of values or countable
number of values, where “countable” refers to
the fact that there might be infinitely many
values, but they result from a counting process
z Continuous
random variable
infinitely many values, and those values can
be associated with measurements on a
continuous scale in such a way that there are
no gaps or interruptions
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
z
Characteristics of the Binomial Distribution:
z
z
z
z
z
z
A trial has only two possible outcomes–“success”or
“failure”
There is a fixed number, n, of identical trials
The trials of the experiment are independentof each
other
The probability of a success, p, remains
constantfrom trial to trial
If p represents the probability of a success, then
(1-p) = q is the probability of a failure
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
zA
manufacturing plant labels items as
either defective or acceptable
z A firm bidding for a contract will either
get the contract or not
z A marketing research firm receives
survey responses of “yes I will buy”or “no
I will not”
z New job applicants either accept the
offer or reject it
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
n!
•
(n – x )!x!
Number of
outcomes with
exactly x
successes
among n trials
px
•
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
qn-x
The probability of
x successes
among n trials
for any one
particular order
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
z
Characteristics of the Poisson Distribution:The
outcomes of interest are rarerelative to the
possible outcomes
z
z
z
The average number of outcomes of interest per
time or space intervalis λ
The number of outcomes of interest are random,
and the occurrence of one outcome does not
influence the chances of another outcome of
interest
The probability thatan outcome of interest occurs in
a given segment is the same for all segments
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
z The
Poisson distribution is sometimes
used to approximate the binomial
distribution when n is large and p is
small.
z n ≥ 100 and np ≤ 10
z Mean = n • p
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
z “n”
trials in a sample taken from a finite
populationof size N
z Sample taken without replacement
z Trials are dependent
z Concerned with finding the probability of
“x”successes in the sample where there
are “X”successes in the population
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
z Use
Excel to test about probability by
using gambling experiment as case
study
z Find the probability to get the “black jack”
if you play only one hand without dealer
(by construct the simulation model in
Excel) and compare to theoretical
calculation
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.
From Business Statistics: A Decision-Making Approach, 7e © 2008 Prentice-Hall, Inc.