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III. Activities
I. Introductory Concept
II. Learning Skills from the MELCs
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Variables can be broadly classified as either quantitative or qualitative, with the former further classified into discrete and continuous types. It is a must for you to understand random variables in such a way that it would be beneficial to the succeeding topics where probability is involved. This activity sheet will help you understand how discrete and continuous random variables differ from each other.
After going through this activity sheet, you are expected to illustrate a random variable (discrete and continuous) (M11/12SP-IIIa-1) ; and distinguish between a discrete and continuous random variable. (M11/12SP-IIIa-2)
Recall that a variable is a characteristic that can assume different values. We use capital letters to denote or represent a variable. In this lesson, this variable is called random variable since it is associated with probabilities.
Suppose you and your friend were tasked to flip a 5-Peso coin once and whoever wins will do a certain task. You choose tail over a head. As you can see from the figure at the right, a tail and a head are random events to happen once you flip a 5-Peso coin. The possible value to substitute for a head is 0 ( zero ) since you did not select it while 1 ( one ) for a tail because you chose it. For these possible values or outcomes to occur, a random variable (let say X ) can be your best representation.
LEARNING ACTIVITY SHEET No. Illustrating and Distinguishing Random Variables (Discrete and Continuous) Week 1 Name of Student: __________________________________________ _____________ Learning Area: STATISTICS AND PROBABILITY Grade Level: _______________ Section: ______________________________________ Date:____________________
ACTIVITY 1: TRANSFER ME CORRECTLY!
In other words, it is a variable which contains the outcomes of a chance experiment. If you will represent T for tail and H for the head in the previous task and let X as your random variable representing the number of tails to occur after flipping a 5-peso coin once, the table below will show you how to illustrate this discrete random variable.
Possible Outcomes Value of the Random Variable X (Number of tail) H 0 T 1 Therefore, the two possible values for a random variable X are 0 and 1. It is denoted as X= { 0, 1} with sample space of S= { H, T }.
On the other hand, there are instances that we cannot count values as a whole but rather we take all considerations to some values in between them, such as fractional or decimal values. In this case, a continuous random variable is made. Observe the illustration given below showing the average speed of a car in a day.
Speed of a car: 55.7 km/h
55 km/h (55.7) 56 km/h
To further give you clear understanding on how to illustrate discrete and continuous random variable, let’s analyze these examples: number of students in the campus the weight or height of the students
Suppose two coins are tossed. Let Y be the random variable representing the number of heads ( H ) that occur. The sample space (S) is provided for you to transfer each element on the possible outcomes column correctly as to the given value of number of heads. Sample Space: S= { HH, HT, TH, HH)
Possible Outcomes Value of the Random Variable Y _(Number of heads) 1.________ 1 _2.________ 2 _3.________ 0 _4.________ 1
5. Thus, the possible values for random variable Y are ( ____, ____ and ____).
there exists a valid value in between them
There are infinite number of possible values, thus it illustrates continuous random variable.
It illustrates an exact and countable value, therefore it is discrete random variable.
VI. References
IV. Rubric for Scoring
ACTIVITY 3 : WHERE DO I BELONG?
V. Answer Key
Classify the following random variables as DISCRETE or CONTINUOUS. Write D for discrete random variable and C for continuous random variable. Write your answer on the blank provided before each number.
_____1. The number of patients a doctor sees in one day _____2. Number of times you check your watch during class _____3. The speed of the car passes on a road every Friday night _____4. The amount of paint utilized in painting your fence in a day _____5. The weight of newborn rabbits each month
ACTIVITY 1 ACTIVITY 2 ACTIVITY 3
- HT or TH
- HH
- TT
- HT or TH
- Thus, the possible values for random variable Y are ( 0,1 and 2 ).
2. DND
4. NND
- Therefore, the possible values for random variable X are ( 0,1 , 2 and 3 ).
1. D
2. D
3. C
4. C
5. C
Belecina, Rene R. et. al (2016). Statistics and Probability.(pp. 1-8) Bluman. Elementary Statistics: A Step by Step Approach, 8th^ Edition (p.6) https://www.google.com/search?q=images+of+cartoon+teachers&rlz=1C 1RLNS_enPH802PH802&hl=en&tbm=isch&source=iu&ictx=1&fir=iveXDhj XShZKM%252CfkRaYqLZAKyHUM%252C_&vet
ACTIVITY 1 ACTIVITY 2 ACTIVITY 3
1 point for every Correct Answer
DEVELOPMENT TEAM OF THE LEARNING ACTIVITY SHEET WRITER : PATERNO P. MAPULA, JR. – Bolo Norte HS MANAGEMENT TEAM/ REVIEWERS : JHOMAR B. JARAVATA- Bula NHS SONIA V. MORAL- Colacling NHS Editor : JUMAR R. VELASCO- RSMOHS Lay-out Artist : JHOMAR B. JARAVATA- Bula NHS Illustrator : PATERNO P. MAPULA, JR. – Bolo Norte HS Validators : DAVID V. ORTIOLA-Laganac HS FROILAN R. DOBLON – San Fernando NHS JOHN EMMANUEL R. IBE- Magarao NHS ROGEL JOHN O. NAVAL-Sta. Cruz NHS
