The document discusses random variables and probability distributions. It defines random variables as functions that assign real numbers to outcomes of statistical experiments determined by chance. Random variables can be discrete, taking on countable values, or continuous, having infinitely many possible values. Examples are provided to illustrate discrete random variables, like the number of heads from coin tosses, and continuous random variables, like calorie intake. The document also distinguishes between discrete and continuous random variables and provides examples of each.

1. Random
Variables and
Probability
Distribution!

2. PRETEST
Direction: Raise your right hand if the statement is correct and your left hand
if the statement is incorrect.
1. Rolling a die has two possible outcomes
2. Random variables can be classified as finite or infinite random variables.
3. Random variable is a way to map outcomes of a statistical experiment
determined by a chance of to number.
4. There are four possible outcomes when four coins are tossed.
5. A random variable can only have one value.

3. Learning Objectives:
At the end of the learning episode, you are expected to:
1. illustrate random variable; and
2. find the possible values of a random variable.
3. illustrate discrete and continuous random variable; and
4. distinguish the difference between discrete and continuous
random variable.

5. Illustrate random variable
Random variable is a function that associates a real number of each
element in the sample space.
Steps on how to determine the random variables in any events or
experiments:
1. Determine the sample space. Assign letters that will represent each
outcome.
2. Count the number of the value of the random variable (capital letter
assigned).

6. Find the possible values of a random variable.
Example 1
Suppose two coins are tossed. Let H represent heads, T represent tails and X
be the random variable representing the number of heads that will occur. Find
the values of the random variable X.
POSSIBLE OUTCOMES VALUE OF THE RANDOM VARIABLE X
So the possible values of random variable X are 0, 1, and 2. We can also
say, X= 0, 1, 2.

7. Example 2
Suppose there are three people to be tested in Covid-19. Let P represent
positive, N represent negative and Z be the random variable representing the
number of infected person that occur. Find the random variable Z.
POSSIBLE OUTCOMES VALUE OF THE RANDOM VARIABLE Z
Find the possible values of a random variable.

8. Example 3
Two winners will be drawn from 5 security guards (S) and 6 canteen staff
(C). Let W be the random variable representing the canteen staff. Find the
values of the random variable W
POSSIBLE OUTCOMES VALUE OF THE RANDOM VARIABLE Z
Find the possible values of a random variable.

9. 1. Three coins are tossed. Let Y be the random variable that represents the number of a tail
that will occur. Find the values of random variable Y.
2. Five computers will be delivered to a certain school for testing, but three of them are
defective. The principal will get two of these computers for his office. Let T represent the
random variable representing the defective computers that will occur. Find the values of
random variable T.

10. Illustrate discrete and
continuous random variable
Were you able to sleep well last night? If so, how long did you sleep?
Did you also take your breakfast today? How many minutes did you
spend at the dining table?
Why am I asking all these questions?
Simply because it has something to do with our lesson today.

11. Two types of random variables:
1. Discrete random variable is a set of possible outcomes that are countable or digital
2. Continuous random variable is a random variable where values are on a continuous scale,
where the data can take infinitely many values such as temperature, weights, and heights.
Distinguish the difference between discrete and
continuous random variables.
Example 1
Suppose a coin is tossed. Heads or tails are the two possible outcomes.
Therefore, this is a discrete random variable.
Example 2
Suppose a teacher surveys her class for the amount of calorie intake of the students’ breakfast.
This is not countable; thus, this is a continuous random variable.

12. Distinguish the difference between discrete and
continuous random variables.
Example 3
Random Variable Classification
Number of planets around the Sun
Number of students in a class
Number of stars in the space
Weight of the students in a particular
class
Range of specified numbers is complete.
Range of specified numbers is
incomplete,
Instruments in a shelf.

13. Classify the following random variables if discrete or continuous.
1. The number of home runs in a baseball game.
2. The speed of cars.
3. The amount of time it takes to sell shoes.
4. The amount of rain, in inches, that falls in a storm.
5. Number of languages an individual speaks.
6. Number of siblings
7. Time to wake up
8. Years of schooling
9. The body temperature of patients with the flu
10.The size of real estate lots in a city

14. In our lesson, we were able to perform a mapping of the
outcomes of a statistical experiment determined by a chance
into numbers. We are dealing here with chances. In life,
managing risk is important especially in our situation now that
we cannot see our enemy. Now it’s up to you to decide as a
young adult to risk or to save lives.

15. A continuous variable can be an unlimited number of values between the
highest to lowest. This data is desirable in statistics; however, in the next
lesson, we will be focusing on discrete variables which are associated
with a limited number of possible values. Just like in life, sometimes we
need to consider the limited resources that we have especially during this
post-pandemic.
Though the financial assistance of our government is continuous at
present, this will never be a lifetime. Same with our decisions in life. Just
like for example the course you are going to pursue in college, you should
determine your choices by ranking 1 up to 10 if you want. This process
illustrates an example of discrete random variables.