ppt02. Random Variable _ Probability Distribution.pptx

Statistics and Probability

1. Exploring Random Variables

2. Lesson Objectives At the end of this lesson, you are expected to: illustrate a random variable; classify random variables as discrete or continuous; and find the possible values of a random variable.

3. Content: Look Back: Probability Entry Card: Sample Space Variable Activity 1: Defective Cell Phones Random Variable Activity 2: Tossing three coins Activity 3: Drawing Balls from an Urn Discrete Random Variable Continuous Random Variable Seatwork Enrichment Assessment

4. Look Back What is Probability? In probability, how do we conduct experiment? Give example. What is outcome? What is sample space?

5. Entry Card List the sample space of the following experiments. Experiment Sample Space 1. Tossing three coins 2. Rolling a die and tossing a coin simultaneously 3. Drawing a spade from a deck of cards 4. Getting a defective item when two items are randomly selected from a box of two defective and three non-defective items 5. Drawing card A, B, and C consecutively.

6. Variable Variable is a characteristic or attribute that can assume different values. Capital letters are use to denote or represent a variable.

7. Activity 1: Defective Cell Phones Supposed three cell phones are tested at random. We want to find out the number of defective cell phones that occur. Thus, to each outcome in the sample space we shall assign a value. These are 0, 1, 2, 3. If there is no defective cell phone, we assign the number 0; if there is 1 defective cell phone, we assign the number 1; if there are two defective cell phones, we assign the number 2; and 3, if there are three defective cell phones.

8. Legend: D= Defective cell phone N= Non-defective cell phone Y= Random variable representing the number of defective cell phones Possible Outcome Value of the Random Variable Y NNN 0 NND 1 NDN 1 DNN 1 NDD 2 DND 2 DDN 2 DDD 3

9. Random Variable A random variable is a function that associates a real number to each elements in sample space. It is a variable whose values are determined by chance.

10. Activity 2: Tossing Three Coins Suppose three coins are tossed. Let X be the random variable representing the number of heads that occur. Find the values of the random variable X. Complete the table. Possible Outcomes Value of the Random Variable X

11. Step 1 Determine the sample space. Let H represent head and T represent Tail. The sample space for this experiment is: S = (TTT, TTH, THT, HTT, HHT, HTH, THH, HHH) Step 2 Count the number of heads in each outcome in the sample space and assign this number to this outcome. Solution:

12. Legend: X = Random variable representing the number of Tails H = Head T = Tail

13. Activity 3: Drawing Balls from an Urn Two balls are drawn in succession without replacement from an urn containing 5 red balls and 6 blue balls. Let Z be the random variable representing the number of blue balls. Find the values of the random variable Z. Complete the table. Possible Outcomes Value of the Random Variable Y

14. Solution: Step 1 Determine the sample space. Let B represent the blue ball and R represent the red ball. The sample space for this experiment is: S = (RR, RB, BR, BB) Step 2 Count the number of blue balls in each outcome in the sample space and assign this number to this outcome.

15. Legend: Z = Random variable representing the number of Blue balls B = Blue ball R = Red ball Possible Outcome Value of the Random Variable Z RR RB BR BB 1 1 2

16. Activity Summary In activity 1, the possible values of random variable Y are 0, 1, 2, and 3. In activity 2, the possible values of random variable X are 0, 1, 2, and 3. In activity 3, the possible values of random variable Z are 0, 1, and 2. Random variables X, Y, and Z are random variables.

17. Discrete Random Variable A random variable is a discrete random variable if its set of possible outcomes is countable. Discrete random variables mostly represent count data, such as number of defective chairs produced in a factory.

18. Continuous Random Variable A random variable is a continuous random variable if it takes on values on a continuous scale. Continuous random variable often represent measured data, such as heights, weights, and temperatures.

19. QUIZ NO. 1 Classify the following random variable as discrete or continuous. The number of voters favoring a candidate. The number of bushels of apples per hectare this year. The average amount of electricity consumed per household per month. The number of death per year attributed to lung cancer The temperature of newly served coffee. The speed of bus. The number of COVID-19 patients aging 60 and above 14. The average weight of new born babies in the 2020 The number of vehicles owned by randomly selected individuals. The average temperature of the costumers in a department store last week as reflected in the logbook.

20. 11. The number of chairs in a room. 12. The amount of rainfall in a day, measured in millimeters. 13. The number of steps a person takes in a day. 14. The length of a piece of string, measured in centimeters. 15. The number of employees in a company. 16. The age of a tree, measured in years. 17. The volume of a liquid in a container, measured in liters. 18. The number of text messages sent in a day. 19. The time spent watching a movie, measured in minutes. 20. The number of apples in a basket. 21. The amount of water in a glass, measured in milliliters. 22. The number of books on a library shelf. 23. The distance traveled by an airplane. 24. The number of goals scored in a soccer match. 25. The price of a product in dollars and cents.

21. GROUP ACTIVITY: Four coins are tossed. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. A shipment of five computers contains two that are slightly defective. If a retailer receives three of these computer at random, list the elements of the sample space S using the letters D and N for defective and non-defective computers, respectively. To each sample point assign a value x of the random variable X representing the number of computers purchased by the retailer which are slightly defective.

22. GROUP ACTIVITY: 3. Let T be a random variable giving the number of heads plus the number of tails in three tosses of a coin. List the elements of sample space S for the three tosses of the coin and assign a value to each sample point. 4. From a box containing 4 black balls and 2 green balls , 8 balls are drawn in succession. Each ball is placed back in the box before the next draw is made. Let G be a random variable representing the number of green balls that occur. Find the value of the random variable G.

23. Individual Activity Look Back and Reflect: How do you find the values of random variable? How do you know whether a random variable is continuous or discrete? What is the difference between continuous and discrete random variable?

24. Thank you for listening…