Statistic anf probability ppt

1. Random Variables,
Probability Distributions,
and Its Properties
STATISTICS AND PROBABILITY

2. Objectives
At the end of the lesson, you should be able to:
1. recognize random variables and their types;
2. differentiate discrete and continuous random variable; and
3. determine the possible values of a random variable.

3. Random Variables
Activity 1

4. Direction: Identify the sample space in each
item.
RE: Tossing two coins
at the same time
RE: Rolling two dice
simultaneously
RE: Drawing a face
card from a deck of
cards
S={HH, HT, TH, TT}
S={(1, 1), (1, 2), (1, 3),
. . . (6, 6)}
S={K , Q , J , K
, …J }

5. Random Experiment
- a process that results in an outcome that cannot be
predicted in advance with certainty
Example
RE: Rolling a die
RE: Tossing two coins at the same time
Sample Space
- set of all possible outcomes
Example
𝑆1 = 1, 2, 3, 4, 5, 6
𝑆2 = {𝐻𝐻, 𝐻𝑇, 𝑇𝐻, 𝑇𝑇}

6. Random
Variable
RE: Tossing two coins at the
same time
S = {HH, HT, TH, TT}
No. of heads:
0, 1, 2,
X: no of heads
x = 0, 1, 2

7. Definition: Random Variable
A random variable is a set whose elements are the
numbers assigned to the outcomes of an experiment. It
is usually denoted by uppercase letters such as X,
whose elements are denoted by lower case letters, x1,
x2, x3 and so on.
X: no of heads
x = 0, 1, 2

8. Types of Random Variables
Discrete Random Variables Continuous Random Variables
number of tails in tossing a coin
thrice
distance leap in meters by a long-
jumper in a competition
number of correct items a student
get in a 10-item test
length of time in minutes that a
scheduled airplane flight is delayed
number of heads in tossing a coin
twice
height of students

9. Types of Random Variables
1. Discrete Random Variable – its set of possible outcomes is countable. Mostly,
discrete random variables represent count data.
Examples
a. number of heads in tossing a coin thrice
b. scores of a student in a 5-item test
2. Continuous Random Variable – its set of possible outcomes takes on values on a
continuous scale. Often, continuous random variables represent measured data.
Examples
a. weight
b. height
c. temperature

10. Study these examples.
Example 1
RE: Tossing a coin thrice
S = {HHH, HHT, HTH, HTT, THH, THT, TTH, TTT}
Y = number of tails
y = 0, 1, 2, 3

11. Example 2
Z = number of correct items a student get in a 10-item
test
z = 0, 1, 2, . . ., 10

12. Example 3
A = drop-out rate (%) in a certain high school
A = {all real numbers from 0 to 100} or {𝑎|0 ≤ 𝑎 ≤ 100}

13. Example 4
B = weight (in mg) of a syrup that does not exceed 80
mg
B = {all real numbers from 0 to 80} or {𝑏|0 ≤ 𝑏 ≤ 80}

14. Note: Examples 1 & 2 are discrete random variables, while
examples 3 & 4 are continuous random variables
Example 1 Y = number of tails y = 0, 1, 2, 3
Example 2 Z = number of correct items z = 0, 1, 2, . . ., 10
a student get in a 10-item test
Example 3 A = drop-out rate (%) in a certain a = {all real numbers from 0 to 100}
high school or {𝑧|0 ≤ 𝑧 ≤ 100}
Example 4 B = weight (in mg) of a syrup that b = {all real numbers from 0 to 80}
does not exceed 80 mg or {𝑏|0 ≤ 𝑏 ≤ 80}

15. Try it!
A. Directions. Identify whether each statement below
represents a discrete random variable or a continuous
random variable.
1. the number of students randomly selected to be
interviewed by a researcher
2. the weight in kilograms of randomly selected
students
3. the hourly temperature last Sunday
4. the number of left-handed teachers randomly
selected in a faculty room
5. the height of daisy plants in the backyard
D
C
C
D
C

16. B. Directions. Give all the possible values of each
random variable as described.
1. X = number of odd number outcomes in a roll of a
die
2. Y = length of a shoelace that is not longer than 2
meter
3. Z = number of heads in a 4 flips of a coin
𝒙 = 𝟎, 𝟏
𝒚 = {𝒂𝒍𝒍 𝒓𝒆𝒂𝒍 𝒏𝒖𝒎𝒃𝒆𝒓𝒔 𝒇𝒓𝒐𝒎 𝟎 𝒕𝒐 𝟐}
𝒛 = 𝟎, 𝟏, 𝟐, 𝟑, 𝟒