1-Illustrates-Random-Varidftgryjyjable.pptx

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1. EXPLORING RANDOM VARIABLES DOMINIC DALTON L. CALING Statistics and Probability | Grade 11

2. 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. LEARNING OBJECTIVES

3. SAMPLE SPACE The set of all possible outcomes of an experiment and represented by the symbol S. It also refers as the population.

4. EXAMPLE S = {HHH, HHT, HTH, THH, TTH, THT, HTT, TTT} S = {1H, 1T, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T} S = {A ♠ , 2 ♠ , 3 ♠ , 4 ♠ , 5 ♠ , 6 ♠, 7 ♠, 8 ♠, 9 ♠, 10 ♠, J ♠, Q ♠, K ♠ } S = {DD, DN, ND, NN} S = {8 ♦ , 9 ♦ , 10 ♦ , J ♦, Q ♦, K ♦, 8 ♥ , 9 ♥ , 10 ♥ , J ♥, Q ♥, K ♥, 8 ♠ , 9 ♠ , 10 ♠ , J ♠, Q ♠, K ♠, 8 ♣ , 9 ♣ , 10 ♣ , J ♣, Q ♣, K ♣ }

5. LESSON INTRODUCTION If three coins are tossed, what numbers can be assigned for the frequency of heads that will occur? If three cards are drawn from a deck, what number can be assigned for the frequency of face cards that will occur? The answers to these questions require an understanding of random variables.

6. DISCUSSION POINTS Suppose 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. Sample Space S = {DDD, DDN, DND, NDD, NND, NDN, DNN, NNN}

7. DISCUSSION POINTS To each outcome in the sample space we shall assign a value. 0 - if there is no defective cell phone 1 - if there is 1 defective cell phone 2 - if there are two defective cell phones 3 - if there are three defective cell phones The number of defective cell phones is a random variable .

8. DISCUSSION POINTS The possible values of this random variable are 0, 1, 2, and 3 .

9. RANDOM VARIABLE A random variable is a function that associates a real number to each element in the sample space. It is a variable whose values are determined by chance.

10. EXAMPLE 1 Tossing Three Coins Suppose three coins are tossed. Let Y be the random variable representing the number of tails that occur. Find the values of the random variable Y. Complete the table below.

11. SOLUTION The possible values of this random variable are 0, 1, 2, and 3 .

12. EXAMPLE 2 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 below.

13. SOLUTION The possible values of th e random variable Z are 0, 1, and 2 .

14. LESSON INTRODUCTION If three coins are tossed, what numbers can be assigned for the frequency of heads that will occur? If three cards are drawn from a deck, what number can be assigned for the frequency of face cards that will occur?

15. DISCRETE RANDOM VARIABLE A random variable is a discrete random variable if its set of possible outcomes is countable. Mostly, discrete random variables represent count data, such as the number of defective chairs produced in a factory. For Example 1, the possible values of random variable Y are 0, 1, 2, and 3. The possible values for random variable Z in Example 2, are 0, 1, and 2. Random variables Y and Z are discrete random variables.

16. CONTINUOUS RANDOM VARIABLE A random variable is a continuous random variable if it takes on values on a continuous scale. Often, continuous random variables represent measured data, such as heights, weights, and temperatures.

17. EXAMPLE OF CONTINUOUS RANDOM VARIABLE Suppose an experiment is conducted to determine the distance that a certain type of car will travel using 10 liters of gasoline over a prescribed test course. If distance is a random variable, then we have an infinite number of distances that cannot be equated to the number of whole numbers. This is an example of a continuous random variable.

18. TRY THIS! Classify the following random variables as discrete or continuous . the number of defective computers produced by a manufacturer the weight of newborns each year in a hospital the number of siblings in a family of a region the amount of paint utilized in a building project the number of dropout in a school district for a period of 10 years discrete discrete discrete continuous continuous

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