Page 1 :
Statistics and, Probability, Quarter 3 – Module 1:, Illustrating a Random Variable, (Discrete and Continuous), , CO_Q3_Statistics and Probability SHS, Module 1

Page 2 :
Lesson, , 1, , Illustrating a Random Variable, (Discrete and Continuous), , This module will assist you with understanding the way toward illustrating random, variables (discrete and continuous). Let’s proceed and appreciate learning., , What’s In, In the study of basic probability, you have discovered that an experiment is any, movement that should be possible more than once under comparative condition. The, arrangement of every possible outcome of an experiment is what we called a sample, space. You have additionally figured out how to mathematically list down the, conceivable outcome of a given experiment. In tossing a coin, for example, the, potential results are turning up heads or tails., For you to begin, let us all understand that probability distributions can be, illustrated or classified as discrete probability distributions or as continuous, probability distributions, depending on whether they define probabilities associated, with discrete variables and continuous variables., A variable X whose value depends on the outcome of a random process is called a, random variable. A random variable is a variable whose value is a numerical outcome, of a random phenomenon., A random variable is denoted with a capital letter. The probability distribution of a, random variable X tells what the possible values of X are and how probabilities are, assigned to those values., A random variable can be discrete or continuous., , 5, , CO_Q3_Statistics and Probability SHS, Module 1

Page 3 :
What’s New, Tossing a coin, As you can see in a one- peso coin, it has Dr. Jose P. Rizal on one side, which we will, call it as heads (H), and the other side is the tails (T). Toss your one-peso coin three, times and record in your notebook the results of the three tosses. In order to write, the result easily, use letter H for the heads and letter T for the tails., If the results of your three tosses are heads, tails, heads, then you will write HTH on, your notebook., Example 1: How many heads appeared when we tossed the one-peso coin three, times?, Continue tossing your coin and record the time. If possible, use mobile phone timer, and record up to the last minute., Let say in a minute, how many times the heads and tails appeared? Then, record all, the possible answers in your notebook., Write all eight possible outcomes. You can do this systematically so that you do not, get confused later on., In this instance, there might be 0 heads, 1 heads, 2 heads or 3 heads., Thus, the sample space is equal to 0, 1, 2, 3., Then this time, the results or outcomes are NOT entirely equally likely., The three coins could land in eight possible ways:, X = Number of Heads, X, , X, TTT, , 0, , THH, , 2, , TTH, , 1, , HTH, , 2, , THT, , 1, , HHT, , 2, , HTT, , 1, , HHH, , 3, , 6, , CO_Q3_Statistics and Probability SHS, Module 1

Page 4 :
Looking at the table we see just 1 case of “three head,” but 3 cases of “two heads,” 3, cases of “one heads,” and 1 case of “zero heads.” So:, •, •, •, •, , P(X=3), P(X=2), P(X=1), P(X=0), , =, =, =, =, , 1/8, 3/8, 3/8, 1/8, , That particular example is a discrete variable. A discrete variable is a variable, which, can only view a countable amount of values. Thus, a discrete random variable X has, possible values 𝑥1 , 𝑥2 , 𝑥3 ....., In graphical form:, , 3/8, , 1/2, , PROBABLITY, , Probability, , 2/8, , 1/4, , 1/4, , 1/8, , 0, , 1, , 2, VALUE, , We can use the probability distribution to answer questions about variable x. In, symbols, we want to find P (X ≥1). We could add probabilities to find the answer:, P(X≥1) = P(X=1) + P(X=2) +P(X=3), 1, , 3, , 3, , 7, , = 8+8+8 = 8, P(X≥1) =1 – P(X < 1) = 1 - P(X = 0), = 1 – 1/8 = 7/8, , 7, , CO_Q3_Statistics and Probability SHS, Module 1

Page 5 :
Example 2;, The probability of each of the possible values for number of heads can be, tabulated for a fair coin tosses twice, as shown:, , Sample space, , Number of Heads, HH, , 2, , HT, , 1, , TH, , TT, , 0, , Number of Heads, , 0, , Probability, , 1/4, , 1, , 2/4, , 2, , 1/4, , or 1/2, Let x be equal to the number of heads observed. x is what we called random variable., •, •, •, , P( X=2) = 1/4, P( X=1) = 2/4, P( X=0) = 1/4, , This is again an example of a discrete variable. Thus, a discrete random variable X, has possible values x1, x2 , x3, ....., , 8, , CO_Q3_Statistics and Probability SHS, Module 1

Page 6 :
In graphical form:, , 2/4, , PROBABLITY, , Probability, , 2/4, , 1/4, , 1/4, , 1/4, , 0, , 1, , 2, , VALUE, , We can use the probability distribution to answer questions about variable x. In, symbols, we want to find P(X ≥1). We could add probabilities to find the answer., P(X≥1) = P(X=1) + P(X=2), 1, , 2, , 3, , = 4+4=4, P(X≥1) =1 – P(X < 1), = 1 – 1/4 = 3/4, Meanwhile, to understand the concept of continuous variable, below are the, examples:, ✓ height of students in class;, ✓ weight of 10 statistics books;, ✓ Time it takes to get to school;, ✓ distance travelled between classes., A continuous variable is a value that is being acquired by measuring., , 9, , CO_Q3_Statistics and Probability SHS, Module 1

Page 7 :
What is It, A Random Variable is a capacity that connects a real number with every component, in the sample space. It is a variable whose qualities are controlled by chance. In this, manner, a random variable is a numerical amount that is derived from the results of, an arbitrary trial or experiment. The word “random” is used often in everyday life., Types of Random Variables, At this point, we can now recognize the two types of arbitrary factors. These are the, discrete and continuous random variables., Discrete random variables are variables which can take on a finite number of, distinct values. Examples are the number of heads acquired while flipping a coin, three times, the number of kin an individual has, the number of students present in, a study hall at a given time, and so forth., You can change the experiment by just flipping a coin twice to make things simpler., Here, the outcomes will be only four: HH, HT, TH, and TT. In addition, the possible, values of X are 0, 1, and 2., Continuous Random Variables, then again, are random variables that take an, interminably uncountable number of potential values, regularly measurable, amounts. Examples are the height or weight of an individual, the time an individual, takes for an individual to wash, time, temperature, item thickness, length, age, etc., For you to better understand the previous activities, another illustration and, examples are shown below., 1. How many outcomes are there in tossing 2 coins? 3 coins? 4 coins?, EVENT, , SAMPLE SPACE, , 2 coins are tossed, , HH, HT, TH, TT, , 3 coins are tossed, , HHH, HHT, THH, THT HTH, HTT, TTH, TTT, HHHH, HHTH, HHTT, HHHT, HTHH, HTHT,, , 4 coins are tossed, , THTT, TTHH, HTTH, HTTT, THHH, THHT,, TTTT, THTH, TTHT, TTTH, , This illustration shows a discrete variable., , 10, , CO_Q3_Statistics and Probability SHS, Module 1

Page 8 :
2. Number of pages in a book is a discrete variable., 3. Time taken to run a race is a continuous variable., 4. Number of matches in a box is a discrete variable., 5. Top speed of a boat is a continuous variable., , What’s More, This comprises activities for independent practice to solidify your understanding and, skills of the topic., Now, answer the following activities below., A. Classify each set of data as discrete or continuous., 1. The height of eggplants., 2. The time it takes the mobile phone to die., 3. The number of students in class., 4. Volleyball scores., 5. The number of cars in the parking area., B. Write letter D if the statement is discrete and letter C if it is continuous, variable., _____1. A container of water., _____2. The height of tomato plants., _____3. Molecules of soft drinks., _____4. The volume of sphere., _____5. The weight of bags of mango., , 11, , CO_Q3_Statistics and Probability SHS, Module 1

Page 9 :
C. Complete the third column by identifying the type of random variable for, each of the given experiment., , Experiment, , Number X or the, Random Variable X, , 1. Recording the number of, hours a specific student use, his/her mobile from 8:00 am, to 5:00 pm for the past three, nights., , The number of hours a, specific student uses, his/her mobile phone, from 8:00 am to 5:00, pm., , 2. Buying two trays of eggs in, the market., , The weight of eggs in, kilograms., , 3. Recording of the gender in a, family with three children., , The number of boys, among the children., , 4. Preparing for a quiz in, Mathematics., , The time a student, spends in reviewing for, this quiz., , 5. Rolling a pair of dice., , The numbers appeared, in a pair of dice., , 12, , Type of Random, Variable, , CO_Q3_Statistics and Probability SHS, Module 1

Page 10 :
What I Have Learned, A. Complete the following statements by writing the correct word., 1. A variable that can be discrete or continuous is ____________________________., 2. A variable whose value is obtained by counting data is called _______________., 3. A variable whose value is obtained by measuring is called __________________., 4. Time it takes to get to school is an example of ______________________________., 5. Number of heads in flipping coins is an example of _________________________., B. 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 asking 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., , 13, , CO_Q3_Statistics and Probability SHS, Module 1

Page 11 :
What I Can Do, Things to do:, Answer the following., Classify whether the given experiment implies a discrete random variable or a, continuous random variable. Write D if discrete and C if continuous., _____ 1. The temperature of a solution in the laboratory., _____ 2. Collecting data about the height of students in a public school., _____ 3. Recording the distance travelled by the bus., _____ 4. Surveying about the number of cases due to COVID-19 pandemic, in Quezon Province., _____ 5. Number of promoted students at the end of school year., , Assessment, Multiple Choice. Choose the letter of the best answer. Write your chosen letter on a, separate sheet of paper., 1. A variable where the information or data can take infinitely many values is:, A. Continuous variable, B. Discrete variable, C. Quantitative, D. Qualitative variable, 2. Which of the following statements describes a continuous random variable?, A. The number of students present in section Temperance., B. The average distance travelled by a tricycle in a month., C. The number of motorcycles owned by randomly selected households., D. The number of girls taller than 5 feet in a random sample of 6 girls., 3. A variable that can be discrete or continuous is called:, A. Random sample, B. Random variable, C. Random notation, D. Random elimination, 14, , CO_Q3_Statistics and Probability SHS, Module 1

Page 12 :
4. Which of the following is a variable whose value is obtained by measuring?, A. Continuous, B. Discrete, C. Interval, D. Normal, 5. Which of the following is NOT a discrete variable?, A. Number of books per student., B. Number of green marbles in the box., C. The number of arrivals of customers in the clinic between 8:00 a.m. to, 4:00 p.m., D. The weight of a case of soft drinks labeled 12 ounces., 6. Which of the following is an example of discrete variable?, A. Distance travelled between cars., B. Height of the students in section Prudence., C. Number of blue marbles in the box., D. Weight of potatoes in the basket., 7. A set of numerical values assigned to a sample space is called:, A. Random experiment, B. Random sample, C. Random variable, D. None of the above, 8. A variable whose value could be a finite and countable number is a:, A. Continuous variable, B. Discrete variable, C. Qualitative variable, D. Quantitative variable, 9. This term can best describe a variable that can be counted., A. Continuous, B. Discrete, C. Interval, D. Ratio, 10. Which of the following is NOT a discrete random variable?, A. Height of eggplant as measured each day., B. Number of refrigerators sold each day., C. Number of late comers in going to school each day., D. Number of people who went to the Rizal Park from Monday to Friday., 11. Which of the following is a discrete random variable?, A. Jose has four sisters., B. Jose is 163 cm tall., C. Jose weighs 68 kilograms., D. Jose ran 300 meters in one and a half minutes ., , 15, , CO_Q3_Statistics and Probability SHS, Module 1

Page 13 :
12. Which of the following is NOT a continuous random variable?, A. The height of the airplane’s flight., B. The amount of liquid on a container., C. The length of time for the check up in the hospital., D. The number of clients of a certain insurance company each day., 13. Which of the following variables is a discrete random variable?, A. The amount of unleaded gasoline in a Suzuki car., B. The temperature of a cup of coffee served at a coffee shop., C. The number of boys in a randomly selected two-child family., D. The average amount spent on electric bill every month of May by a, randomly selected household in Quezon Province., 14. You decided to conduct a survey of families with three children. You are, interested in counting the number of girl in each family. Is this a random, variable?, A. Yes, it is a random variable., B. No, it is not a random variable., C. Maybe, it is a random variable., D. It cannot be determined., 15. Which of the following statements DOES NOT describe a continuous random, variable?, A. Height of students in a certain class., B. The average weight of chicken each day., C. The number of streets at barangay Tahimik., D. The distance travelled by a delivery van in an hour., , 16, , CO_Q3_Statistics and Probability SHS, Module 1

Page 14 :
Additional Activities, , Hondagua National High School-Senior High School would like to conduct election, for the Accountancy, Business, and Management (ABM) officers. Complete the table, for the possible outcomes from a sample of four voters and identify also the value of, random variable of the number of “yes” votes., Event Voter # 1, , Voter #2, , Voter #3, , Voter #4, , Value of Random, Variables, (Number of Yes votes), , 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, , 17, , CO_Q3_Statistics and Probability SHS, Module 1