The document outlines various exercises for unscrambling words and defines random experiments and variables. It distinguishes between discrete and continuous random variables, providing examples to illustrate the concepts. The objective is to help readers understand the nature of these random variables through practical scenarios.

1. `

2. Unscramble the following words
The first and the last letters are written properly
SPALME

3. Unscramble the following words
The first and the last letters are written properly
SPALME
SAMPLE

4. Unscramble the following words
The first and the last letters are written properly
COUTINONUS

5. Unscramble the following words
The first and the last letters are written properly
COUTINONUS
CONTINUOUS

6. Unscramble the following words
The first and the last letters are written properly
DCSITERE

7. Unscramble the following words
The first and the last letters are written properly
DCSITERE
DISCRETE

8. Unscramble the following words
The first and the last letters are written properly
FITINE

9. Unscramble the following words
The first and the last letters are written properly
FITINE
FINITE

10. Unscramble the following words
The first and the last letters are written properly
VIABARLE

11. Unscramble the following words
The first and the last letters are written properly
VIABARLE
VARIABLE

12. Unscramble the following words
The first and the last letters are written properly
IFNITINE

13. Unscramble the following words
The first and the last letters are written properly
IFNITINE
INFINITE

14. Unscramble the following words
The first and the last letters are written properly
RADNOM

15. Unscramble the following words
The first and the last letters are written properly
RADNOM
RANDOM

16. Unscramble the following words
The first and the last letters are written properly
VUELAS

17. Unscramble the following words
The first and the last letters are written properly
VUELAS
VALUES

18. Unscramble the following words
The first and the last letters are written properly
CATONLUBE

19. Unscramble the following words
The first and the last letters are written properly
CATONLUBE
COUNTABLE

20. RANDOM VARIABLES
A random experiment is any
process or procedure that can
be repeated under general same
conditions (repetition) and the
result, called the outcome, can
only be known after the
experiment is over (uncertainty)
Definition 1.1.1
For any given random
experiment, there is a nonempty
set of all possible outcomes
called the sample space, denoted
by S

21. RANDOM VARIABLES
Example 1
tossing of a fair coin
tossing of two fair coins
tossing of three fair coins
Example 2
Suppose an experiment is
performed by rolling a fair six-
sided die indefinitely until three-
dotted face occurs.

22. RANDOM VARIABLES
Example 3
An experimenter wants to know the maximum temperature , in
degrees Celsius, at a particular day for the month of November. Based
on previous readings, it is known that November temperature ranges
from 30 to 36 degrees Celsius

23. RANDOM VARIABLES
Example 1
tossing of a fair coin
tossing of two fair coins
tossing of three fair coins
Example 2
Suppose an experiment is
performed by rolling a fair six-
sided die indefinitely until three-
dotted face occurs.

24. RANDOM VARIABLES
Example 3
An experimenter wants to know the maximum temperature , in
degrees Celsius, at a particular day for the month of November. Based
on previous readings, it is known that November temperature ranges
from 30 to 36 degrees Celsius

25. RANDOM VARIABLEs
Objective:
• distinguish between a discrete and a continuous random variable.
• find possible values of random variable

26. DISCRETE AND CONTINUOUS RANDOM VARIABLE
A discrete random variable is
one that can assume only a
countable number of values. It is
a random variable whose
possible values form a finite or
countable set of numbers.
A continuous random variable
can assume infinite number of
values in one or more intervals. A
continuous random variable is
generated from an experiment in
which things are counted but not
measured

27. DISCRETE AND CONTINUOUS RANDOM VARIABLE
Group game.
1. The number of senators present in the meeting -
2. The weight of newborn babies for the month of June -
3. The number of ballpens in a box -
4. The capacity of electrical resistors -
5. The amount of salt needed to bake a loaf of cake -
6. The capacity of an auditorium -
7. The number of households with television -
8. The height of mango trees in a farm -
9. The area of lots in a subdivision -
10. The number students who joined the field trip -

28. VALUES OF RANDOM VARIABLE
Example 1
Suppose two coins are tossed and we are interested to determine the
number of heads that will come out. Let us use H to represent the
number of heads that will come out. Determine the values of the
random variable H
Steps
1. List the sample space of the experiment
2. Count the number of heads in each outcome and assign the
number to this outcome

29. VALUES OF RANDOM VARIABLE
Step 1. List the sample space of the experiment
S = 𝐻𝐻, 𝐻𝑇, 𝑇𝐻, 𝑇𝑇
Step 2. Count the number of heads in each outcome and assign this
number to this outcome
Therefore, the values of the random variable H are 0, 1, and 2
OUTCOME NUMBER OF HEADS
(Value of H)
HH 2
TH 1
HT 1
TT 0

30. VALUES OF RANDOM VARIABLE
Example 2
A basket containing 10 ripe and 4 unripe bananas.
If three bananas are taken from the basket one
after the other, determine the possible values of
the random variable R representing the number
of ripe bananas

31. PAIRWORK
1. A meeting of consuls was attended by four
Americans and two Germans. If three consuls were
selected at random one after the other. Determine
the values of the random variable G representing
the number of Germans.
2. Three coins are tossed. Let T be the number of tails
that occurs. Determine the values of the random
variable T