lesson

1. REVIEW
• Random Variable
• Types of Random Variable
1. Discrete Random Variable
2. Continuous Random Variable

2. Motivation
RANDOM VARIABLE (X) Values (x) of
Random Variable X
1. The number of boys in a family of 3 children
2. The temperature in Bucay, Abra on a particular
day
3. The percentage of SHS students who were
dropped last semester
4. The age of senior high school students of
CBGMHS
5. The number of students visited in the Guidance
Office

3. EXAMPLE:

4. • A fair coin is turned vertically on a flat
surface.
Here are two related random variables.
 Let X be the time between the commencement of
the spin and the coin coming to rest , measured
in seconds.
 Let Y be the number of tails showing when the
coin come to rest . Then Y, takes the value 0 if
the coin finishes up ”heads”, or 1 if the coin
finishes up “tails”
 Here, X is continuous and Y is discrete

5. DISCRETE RANDOM
PROBABILITY
DISTRIBUTION
BONIE C. SANCHEZ

6. OBJECTIVES:
• Find the possible values of a
random variable
• Illustrate a probability distribution
for a discrete random variable
• Construct a discrete probability
distribution

7. Discrete Random Probability
Distribution
The probability distribution of a
discrete random variable, X, is a list
of all possible values of x can
take and the associated
probabilities.

8. Notation:
0 ≤ P(x) ≤ 1

9. • The sum of all the probabilities in the
probability distribution is 1
• In Notation
• The capital Greek letter sigma (∑) denotes
summation
∑ P(x) = 1

10. Guidelines in Constructing a
Discrete Probability
Distribution

11. Example 1:
• A coin is tossed twice . Let X
be the number of heads
observed in tossing of the
coin.
• Construct a probability
distribution of the random
variable X.

12. Solution:

13. FREQUENCY DISTRIBUTION

14. Computing the probability of
each outcome
1. Sum of the frequencies of outcomes is 4
2. Probability of each outcome
a. Probability of getting no head
b. Probability of getting 1 head
c. Probability of getting 2heads
3.

15. PROBABILITY DISTRIBUTION

16. Relative Frequency Histogram
of the Probability Distribution

17. Example 2:

18. Solution:

19. Solution:

20. Solution:

22. Relative Frequency Histogram