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 eventThe probability of each outcome is between 0 and 1The 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:

Suppose we are interested in the number of the heads showing face up. The table above can be modified to:

Possible outcomes First Second1 T T

2 T H

3 H H

4 H T

Possible outcomes First Second Number of Heads1 T T 0

2 T H 1

3 H H 2

4 H T 1

Construct the Probability Distribution table

Number of Heads(x) Probability of Outcome(p(x))

0 ¼=0.25

1 2/4=0.5

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 DistributionThe 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

distributionb. Compute the standard deviation of the

probability distribution

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$

Price of Modem(x) Probability (p(x)) x.P(x)

25$ 0.20 5

30$ 0.50 15

35$ 0.30 10.5

Exercises1. The following is the probability distribution for cash prizes in a lottery

conducted at CTN radio station.

a. If you buy one ticket, what is the probability that you win at least 100,000 riel?

b. Compute the mean and standard deviation of this distribution.

Prize(riel) Probability

0 0.40

20,000 0.30

100,000 0.20

400,000 0.15

1,000,000 0.5