This document provides steps for constructing a discrete probability distribution: 1) Assign letters to represent each possible outcome 2) Determine the sample space of all possible outcomes 3) Count the number of occurrences of each value of the random variable 4) Calculate the probability of each value by dividing its frequency by the total number of possible outcomes It then provides two examples: tossing three coins and summing the outcomes of rolling two dice, to illustrate constructing probability distributions and histograms.

2. D I S C R E T E P R O B A B I L I T Y D I S T R I B U T I O N
•
•

3. Steps in getting the probability of each value of the
random variable:
• Assign letters that will represent each outcome.
• Determine the sample space (possible outcomes).
• count the number of the value of the random variable.
• Given the total possible values of the random variable,
assign probability values to each value of the random
variable.

4. Suppose three coins are tossed.
Let X be the random variable
representing the number of heads.
Construct the probability
distribution and draw the
histogram.

5. HHH
HHT
HTT
HTH
THH
TTH
THT
TT
T
3
2
2
2
1
1
0
1
Possible
Outcome
s
Value of the random
variable, X
no. of Heads, X
Probability, P (X)
0 1 2 3
1/
8
3/8 3/8 1/
8
SOLUTION: Probability Distribution
X
1/8
2/8
3/8
4/8
P(X
)

6. Two Fair dice are thrown
simultaneously. Let X be the sum
of the two outcomes in throwing
the two fair dice. Construct a
probability distribution. Draw the
histogram.

7. 0 p(x) 1
P R O P E R T I E S O F A D I S C R E T E
P R O B A B I L I T Y D I S T R I B U T I O N
p(x) =1

8. not probability
distribution
Discrete Probability
Distribution

9. Provide space for more
examples