January 27 2025 - 4 - LESSON 3 - CO3 - STATISTICS AND PROBABILITY - EXPLORING RANDOM VARIABLES LESSON 3.pptx

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1. CONSTRUCTING PROBABILITY DISTRIBUTION LESSON 3 Ping Ignacio

2. Play Time!

3. Play Time! Game Link

4. Can data be classified as countable or measurable ?

5. How will you represent data and other information in your research subject?

6. Lesson Objective Constructs the probability mass function of a discrete random variable and its corresponding histogram.

7. By Groups Let T be a random variable giving the number of heads in tossing 3 coins. List the elements of the sample space S for tossing 3 coins and find the probability of each of the values of the random variable T . (10min)

8. STEPS SOLUTION Determine the sample space. Activity (Group 1) Let T be a random variable giving the number of heads in tossing 3 coins. List the elements of the sample space S for tossing 3 coins and find the probability of each of the values of the random variable T.

9. STEPS SOLUTION Count the number of heads in each outcome in the sample space and assign this number to this outcome. Activity (Group 2) Let T be a random variable giving the number of heads in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and find the probability of each of the values of the random variable T.

10. STEPS SOLUTION Write the number of possible values and assign probability values to each random variable. Activity (Group 3) Let T be a random variable giving the number of heads in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and find the probability of each of the values of the random variable T.

11. Answers

12. STEPS SOLUTION Determine the sample space. S= {TTT, TTH,THT,HTT,HHT,HTH, THH,HHH)} Activity (Group 1) Let T be a random variable giving the number of heads in tossing 3 coins. List the elements of the sample space S for tossing 3 coins and find the probability of each of the values of the random variable T.

13. STEPS SOLUTION Count the number of heads in each outcome in the sample space and assign this number to this outcome. Activity (Group 2) Let T be a random variable giving the number of heads in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and find the probability of each of the values of the random variable T.

14. STEPS SOLUTION Write the number of possible values and assign probability values to each random variable. Activity (Group 3) Let T be a random variable giving the number of heads in three tosses of a coin. List the elements of the sample space S for the three tosses of the coin and find the probability of each of the values of the random variable T.

15. Make a probability Mass Function of Discrete Random Variable T.

16. Construct a Histogram

17. Construct a Histogram

18. Construct a Histogram

19. Construct a Histogram

20. Construct a Histogram

21. CONSTRUCTING PROBABILITY DISTRIBUTION LESSON 3 Ping Ignacio

22. Activity Two balls are drawn 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.

23. STEPS SOLUTION Determine the sample space. Activity 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. STEPS SOLUTION Determine the sample space. S = { RR, RB, BR, BB } Activity 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.

25. STEPS SOLUTION Count the number of blue balls in each outcome in the sample space and assign this number to this outcome. Activity 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.

26. STEPS SOLUTION Count the number of blue balls in each outcome in the sample space and assign this number to this outcome. Activity 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.

27. STEPS SOLUTION Write the number of possible values and assign probability values to each random variable Activity 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.

28. STEPS SOLUTION Write the number of possible values and assign probability values to each random variable Activity 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.

29. Make a probability Mass Function of Discrete Random Variable Z.

30. Construct a Histogram

31. CONSTRUCTING PROBABILITY DISTRIBUTION LESSON 3 Ping Ignacio

32. Practical Application The daily demand for copies of a newspaper at a variety store has the probability distribution as follows:

33. Practical Application The daily demand for copies of a newspaper at a variety store has the probability distribution as follows: What is the probability that the demand will be two or more? 0.8 or 80 %

34. Practical Application The daily demand for copies of a newspaper at a variety store has the probability distribution as follows: What is the probability that the demand will be at least two but not more than six? 0.6 or 60%

35. CONSTRUCTING PROBABILITY DISTRIBUTION LESSON 3 Ping Ignacio

36. Activity The following data show the probabilities for the number of Banana Chipssold in SHS Canteen: a. Find P(X≤ 2) b. Find P(X≥ 7) c. Find P(1≤ X ≤ 5) Assignment: d. Construct a histogram

37. Activity The following data show the probabilities for the number of Banana Chipssold in SHS Canteen: a. Find P(X≤ 2) =0.5 b. Find P(X≥ 7)=0.13 c. Find P(1≤ X ≤ 5)= 0.71 or 71%

38. CONSTRUCTING PROBABILITY DISTRIBUTION LESSON 3 Ping Ignacio

39. Activity The following data show the probabilities for the number of Banana Chipssold in SHS Canteen: a. Find P(X≤ 2) =0.5 b. Find P(X≥ 7)=0.13 c. Find P(1≤ X ≤ 5)= 0.71 or 71% d. Construct a histogram

40. Activity In a game, a bag contains 8 green marbles and 7 yellow marbles . Two marbles are drawn from the bag. Let the random variable Z represent the number of yellow marbles drawn. Construct the probability distribution of the random variable Z.