Download Chapter 5: Probability Distribution

Chapter 5: Probability Distribution
What is Probability Distribution?
 It is a table of possible outcomes of an
experiment and the probability of each outcome.
 It describes the chance of the future event
 The probability of each outcome is between 0
and 1
 The sum of all mutually exclusive possible
outcomes is 1.
Example: In tossing a coin two times, the possible
outcomes can written in the table below:
Possible outcomes
First
Second
1
T
T
2
T
H
3
H
H
4
H
T
Possible outcomes
First
Second
Number of Heads
1
T
T
0
3
H
H
2
4
H
T
1
Suppose we are interested in the number of the heads showing face up. The
2
T
H
1
table
above can be modified
to:
Number of Heads(x)
Probability of Outcome(p(x))
0
¼=0.25
1
Construct
the Probability Distribution 2/4=0.5
table
2
¼=0.25
The graph of the number of heads resulting from tossing one coin two
times.
The mean, and Standard Deviation of a Probability
Distribution
The mean is the weighted average of the
probability distribution.
It represents the typical value used to summarize
the probability distribution.
The mean can be called expected value, E(x).
The mean of the probability distribution can be
expressed in the following formula:
μ=E(x)= ∑[xp(x)] where x is the random variable,
and p(x) is the probability of x.
Note: A random variable is a variable can assume
different random values. In tossing a coin, if x is the
variable that can assume different outcomes such as
1 head, 1 tail, 0 head, 0 tail, x is called random
variable.
Standard Deviation describe the amount of spread
in a probability distribution.
It can be expressed by the following formula:
ϭ=(∑[(x-μ)2p(x)])1/2
Example: A retail computer shop every day sells
three types of internet modems—A, B, and C. They
are sold for 25$, 30$, and 35$ respectively. The
probability the next A modem purchase is 0.30, 0.
50 B purchase, and 0.20 C purchase.
a. Compute the mean of the probability
distribution
b. Compute the standard deviation of the
probability distribution
Price of Modem(x)
Probability (p(x))
x.P(x)
25$
0.20
5
30$
0.50
15
0.30
10.5
35$
Solution:
a. E(x)=5+15+10.5=30.5$
b. Ϭ=((25-30.5)2*0.20+(30-30.5)2*0.50+(35-30.5)2*0.30)1/2
=3.5$
Exercises
1. The following is the probability distribution for cash prizes in a lottery
conducted at CTN radio station.
a.
b.
Prize(riel)
Probability
0
0.40
20,000
0.30
100,000
0.20
400,000
0.15
1,000,000
0.5
If you buy one ticket, what is the probability that you win at least
100,000 riel?
Compute the mean and standard deviation of this distribution.