PPT-3_Q1_Constructing-Probability-Distribution-for-Random-Variables.pptx

Probability is the measure of how likely an event is to occur. It ranges from 0 (impossible event) to 1 (certain event). The construction of probability involves defining the sample space, identifying favorable outcomes, and applying probability rules.

1. PRAYER

2. CHECKING OF ATTENDANCE

3. HOUSE RULES Be focused. Be an active listener and be ready to take down notes. Participate in the class discussion. Respect one another. Keep your cellphone inside your bag.

4. NUMERACY INTERVENTION

5. PROBLEMS INVOLVING INTEGERS A seller gained Php 99.00 for selling bread and Php 80.00 for selling buko juice. How much was her total gains?

6. PROBLEMS INVOLVING INTEGERS Alex went shopping and parked his car in a garage 4 floors below the ground level. Then, he took the elevator and went up 16 floors more. On what floor did Alex get off the elevator?

7. PROBLEMS INVOLVING INTEGERS For the past 5 years, the population of a city has decreased by 16 people a year. What was the city’s decrease in population 5 years ago?

8. PROBLEMS INVOLVING INTEGERS During a 12-hour period, the temperature dropped 48⁰F. How many degrees did the temperature drop each hour?

9. STATISTICS AND PROBABILITY

10. GETTING READY

11. Constructing Probability Distribution for Random Variables

12. Learning Objectives At the end of this lesson, you are expected to: illustrate a probability distribution for discrete random variable and its properties. construct the probability mass function of a discrete random variable. compute probabilities corresponding to a given random variable.

13. Discrete Probability Distribution 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.

14. Properties of Probability Distribution The probability of each value of the random variable must be between or equal to 0 and 1. In symbol, we write 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  

15. 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 by completing the table with the given steps. Illustrative Example

16. SOLUTION

17. SOLUTION

18. What do you notice about the probability of each value of the random variable? Write your conclusion regarding this matter. Get the sum of the probabilities of all values of the random variable. What sum did you get? Write your conclusion regarding this matter. ANALYSIS

19. What is a discrete probability distribution or a probability mass function? ABSTRACTION

20. Discrete Probability Distribution 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.

21. What are the properties of a probability distribution? ABSTRACTION

22. Properties of Probability Distribution The probability of each value of the random variable must be between or equal to 0 and 1. In symbol, we write 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  

23. APPLICATION Number of Blue Balls 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. Construct the probability distribution of the random variable Z.

24. 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 cell phone and N represent the non-defective cell phone. Let X be the random variable representing the number of defective cell phones. Construct the probability distribution of the random variable X. ASSESSMENT

25. A shipment of five computers contains two that are slightly defective. If a retailer receives three of these computers at random, list the element of the sample space S using the letters D and N for defective and non-defective computers, respectively. Let X be the random variable representing the number of computers purchased by the retailer which are slightly damaged. Construct the probability distribution of the random variable X. ASSIGNMENT