Understanding Random Variables: Discrete and Continuous Types, Lecture notes of Statistics

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Illustrating a Random

Variable

DISCRETE AND CONTINUOUS

Types of Random

Variables

Discrete Random Variable – is variable can

take on a finite (countable) number of distinct

values.

Continuous Random Variable – is a variable

can take an interminably uncountable number

of potential values, regularly measurable

amounts.

Examples of Random Variable

Experiment

Number X

or the

Random

Variable X

Types of

Random

Variable

1. Record the number of hours an specific use their mobile from 8:00 am to 5 pm for the past three nights
2. Buying two trays of egg in the market
3. Recording of the gender of family members in a family with three children
4. Students will prepare for a quiz in Mathematics
5. Rolling a pair of dice

Random Variable – is a numerical quantity that is derived from the outcome of a random experiment.

Example 1:

In a box, there are 2 balls – one white and yellow. Two balls

are picked one at a time with replacement. Let X be the

random variable representing the number of white balls. Find

the values of the random variable X.

1. Determine the sample space. Let W represent the white

ball and Y for the yellow ball.

2. Count the number of white balls in each outcome I the

sample space and assign this number to this outcome.

Possible Outcomes Value of the random variable X (Number of white balls) WW 2 YY 0 WY 1 YW 1 So, the possible values of the random variable X are 0, 1, and 2.

A. Complete the table below.

Experiment Number X or the Random Variable X Types of Random Variable

1. Number of rings before the phone is answered
2. Teacher ask the students to finish the test after an hour
3. Number of complaints per day
4. Height of the tallest building in Lucena City
5. Number of mobile phones in a household