Discrete random variable Statistics and Probability.pptx

discrete random variable

1. GENERAL MATHEMATICS for SENIOR HIGH SCHOOL

2. Preliminary Activities Opening Prayer

3. Opening Prayer Heavenly Father and Your Beloved Son Jesus Christ, Thank you for another day of being able to go to school and learn new set of things we will experience in our classes today. As we go through our class at this moment, give us wisdom to understand the lessons that we will be discussing this afternoon. Help us to be obedient, honest, and kind to one another. Bless our teachers, our school and my fellow students. In Jesus’ name we pray. Amen.

4. 2. Checking of Attendance

5. Preliminary Activities Math Puzzle

6. 45 -12 -7 -45 -5 57 -45 -15 -5 1. 2. 3. 4. 5. 6. 7. 8. 60 33 -9 -225 -12 -1 -315

7. L ESSON OBJECTIVES: At the end of t he period , the students with 80% accuracy, are expected to: Know what is a probability distribution for a discrete random variable and its properties; compute probabilities corresponding to a given random variable; and construct the probability mass function of a discrete random variable

8. REVIEW: DISCRETE VARIABLES CONTINUOUS VARIABLES VS

9. REVIEW: DISCRETE VARIABLES CONTINUOUS VARIABLES VS VARIABLES THAT CANNOT TAKE THE FORM OF DECIMALS CAN BE COUNTED VARIABLES THAT CAN TAKE THE FORM OF DECIMALS CAN BE MEASURED

10. REVIEW: DISCRETE VARIABLES CONTINUOUS VARIABLES VS VARIABLES THAT CANNOT TAKE THE FORM OF DECIMALS CAN BE COUNTED VARIABLES THAT CAN TAKE THE FORM OF DECIMALS CAN BE MEASURED

11. REVIEW: Which of the following statements is considered a DISCRETE or CONTINUOUS data. The harvest package received second week was 4.3 kilos. The maximum temperature in Metro Manila on Jan. 21,2018 according to the weather newscaster was 34.2 degree Celcius In the City of Cebu, a total of 25 fires were reported by the Cebu City Fire Department to have occurred during the year 2015. Dr. Cano’s reported income for the past year was P530,855.43 per annum. Only 345 applicants passed the College of Education Entrance Test in Cebu Normal University

12. REVIEW: FINDING POSSIBLE VALUES OF RANDOM VARIABLES: STEPS: To determine the sample space/number possible outcome, use where n is refers to number of an object. Make a table. Identify the possible values of the random variable.  

13. Decision-making is an important aspect in business, education, insurance, and other real-life situations. Many decisions are made by assigning probabilities to all possible outcomes pertaining to the situation and then evaluating the results. For instance, an insurance company might be able to assign probabilities to the number of vehicles a family owns. This information will help the company in making decisions regarding future financial situations. This situation requires the use of random variables and probability distribution. Ask: How does probability distribution relates to real-life situation? Lesson Introduction:

14. DISCUSSION ON DISCRETE PROBABILITY DISTRIBUTION

15. DISCRETE PROBABILITY DISTRIBUTION Also known as probability mass function consists of the values of random variable can assume and the corresponding probabilities of the values.

16. DISCRETE PROBABILITY DISTRIBUTION Properties: The probability of each value of the random variable must be between or equal to 0 and 1. The sum of the probability of all values of the random variable must be equal to 1

17. Illustrative Example: Finding the probability corresponding to a given random variable Experiment #1: Drawing balls from a basket Two balls are drawn in succession without replacements from a basket, contains 4 yellow balls and 4 blue balls . Let X be the random variable representing the number of blue balls , Find the values of the random variable X .

18. Step 1: Determine the sample space Step 2: List the possible outcome Step 3: Count the number of the variable asked in the experiment in each outcome in the sample space and assign this number to this outcome Finally, Given the values of the possible outcomes, solve/compute the probability P of each value of the random variable. Discussion Points:

19. The Probability Distribution or the Probability Mass Function of Discrete Random Variable Z Solution to Experiment #1

20. Group Activity Finding the probability corresponding to a given random variable Experiment # 2: Tossing Three Coins Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the probability of each of the values of the random variable Y .

21. Group Activity Finding the probability corresponding to a given random variable Experiment # 3: Defective Cellphones Suppose three cell phones are tested at random. We want to find out the number of defective cell phones that occur. Let D represent the defective cellphone and N represent the non-defective cellphone . Let X be the random variable representing the number of defective cellphones . Construct the probability distribution of the random variable X .

22. Solution to Experiment # 2 Probability Distribution or Probability Mass function of Discrete Random Variable X Continuation Step 3

23. A discrete probability distribution or a probability mass function consists of the values a random variable can assume and the corresponding probabilities of the values. Summary:

24. Properties of a Probability Distribution The probability of each value of the random variable must be between or equal to 0 and 1. In symbol, we write it as 0 ≤ P(X) ≤ 1. The sum of the probabilities of all values of the random variable must be equal to 1. In symbol, we write it as ∑P(X) = 1. Summary:

25. Step 1: Determine the sample space Step 2: List the possible outcome Step 3: Count the number of the variable asked in the experiment in each outcome in the sample space and assign this number to this outcome Finally, Given the values of the possible outcomes, solve/compute the probability P of each value of the random variable. Summary:

26. Assessment The students will answer Worksheet 3.4 Checking of answers will follow. Feedbacking of results and difficulties

27. Assignment The students will answer Activity 3.2 and Activity 3.3 pages 14 and 15 in their Module. To be submitted next meeting

28. THOUGHTS TO PONDER:

29. End Activity Closing Prayer