1. Random Variables and Probability Distribution (1)
Definition: A random variable is a function that associates a real number with each element in the sample space.
A random variable symbol should be capital letter such X, Y, … and its corresponding is small letter.

2. Random Variables and Probability Distribution (1)
Example: Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 black balls. The possible outcomes and the value Y of the random variable Y where Y is the number of red balls are:
Sample space “S”: [RR, RB, BR, BB]
Number of reds “Y”: [2, 1, 1, 0]

3. Random Variables and Probability Distribution (1)
Definition:
If a sample space contains a finite number of possibilities or an unending sequence with as many elements as there are whole numbers, it is called a discrete sample space.

4. Random Variables and Probability Distribution (1)
Definition:
If a sample space contains an infinite number of possibilities equal to the number of points on a line segment, it is called a continuous sample space.

5. Random Variables and Probability Distribution (1)
Example: Classify the following random variables are discrete or continuous:
X: The number of automobile accidents?
It is discrete random variable.
Y: The length of time to play 18 holes of Golf?
It is continuous random variable.
M: The mount of milk produced yearly by a particular cow?

6. Random Variables and Probability Distribution (1)
Example:
N: The number of eggs laid each month by a hen?
It is discrete random variable.
P: The number of building permits issued each monthly in a certain city?
Q: The weight of grain produced per acre?
It is continuous random variable.

7. Random Variables and Probability Distribution (1)
Discrete Probability Distribution
Definition :
The set of ordered pairs (x, f(x)) is a probability function, probability mass function or probability distribution of the discrete random variable X if for each possible outcome x ;

8. Random Variables and Probability Distribution (1)As

9. Random Variables and Probability Distribution (1)
Example (1):
A shipment of 20 similar laptop computers to a retail outlet contains 3 that are defective. If a school makes a random purchase of 2 of these computers, find the probability distribution for the number of defectives.

10. Random Variables and Probability Distribution (1)
Solution:
Let X be a random variable whose values x are the possible numbers of defective computers purchased by the school. Then x can only take the numbers 0, 1, 2 then:

11. Random Variables and Probability Distribution (1)2.

12. Random Variables and Probability Distribution (1)
Then the probability distribution is X 1 2
f(x)
68/95
51/190
3/190

13. Random Variables and Probability Distribution (1)
Example2:
Suppose X is the sum of up faces of 2 dies:

14. Random Variables and Probability Distribution (1)
X: sum of up faces of 2 dies 1 2 3 4 5 6 7 8 9 10 11 12

15. Random Variables and Probability Distribution (1)X
f(x) = P (X=x) 2
1/36  3
 2/36 4
3/36 5
 4/36 6
 5/36 7
 6/36 8 9 10
 3/36 11 12
 1/36
The probability distribution function table is

16. Random Variables and Probability Distribution (1)
Then