Chapter I Random Variables and Probability Distribution PDF

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A B C DA B C DA B C DSelf-Learning Module for Grade 11Mathematics Statistics and ProbabilityCHAPTER I: RANDOM VARIABLES AND PROBABILITY DISTRIBUTION LESSON 1: RANDOM VARIABLE (Discrete and Continuous)In the study of basic probability, you have learned that an experiment is any activity which can be ...

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Self-Learning Module for Grade 11 Mathematics Statistics and Probability CHAPTER I: RANDOM VARIABLES AND PROBABILITY DISTRIBUTION LESSON 1: RANDOM VARIABLE (Discrete and Continuous) Introduction In the study of basic probability, you have learned that an experiment is any activity which can be done repeatedly under similar condition. The set of all possible outcomes of an experiment is called the sample space. You have also learned how to mathematically list the possible outcome of a given experiment. In tossing a coin, for instance, the possible outcomes are turning up a head or a tail. This module will help you understand the process of illustrating random variables as well as distinguishing between discrete and continuous random variables. God bless and enjoy learning.

How to Use this Module This Self - learning Kit (SLK) will help you understand the concepts on Random Variables. As you go through this lesson, think of the following questions: How will you distinguish random variables as to discrete or continuous? To find the answer, perform each activity. PRE-TEST

Before studying this module, take this pre - test to find out how much you already know about the topic covered. Shade the letter of the correct answer. 1. Discrete variable is from qualities that can be A. Measured C. Both A and B A B C D B. Counted D. none of these `

2. Continuous variable is from qualities that can be A. Measured C. Both A and B A B C D B. Counted D. none of these 3. Which of the following is NOT a continuous variable? A. A person’s height each year A B C D B. A person’s weight on each birthday C. Number of Cars finished in a factory each day D. The volume of water in a swimming pool

4. Which of these is NOT a discrete variable? A. The number of students absent in a class A B C D B. The number of death per year attributed to lung cancer C. The average amount of electricity consumed per household per month D. The number of people who drive through a red light each hour during rush hour 5. The number of avocado produced by an avocado tree each year is a continuous variable A B C D A. True C. Maybe B. False D. Cannot be determined Well, what do you think about the pre-test? Do you think you did well? Compare your answers with those in the Answer Key on the last part of this module to find out. If all your answers are correct, excellent! This shows that you already know much about the topic. But you may still study this module to check what you already know. Who knows, you might learn a few more new things as well. If you got a low score, it’s ok. This module was made to help you understand important concepts about random variable that you can apply in your daily life. If you study this module carefully, you will learn the answers to all the items in the test and a lot more! Are you ready? Let’s begin your journey.

Competency 1. Illustrate random variable (Discrete or Continuous). (M 11/12 SP IIIa – 1) 2. Distinguish between a discrete and a continuous random variable. (M11/12 SP IIIa – 2) Objective At the end of this lesson, you should be able to: 1. Illustrate random variable; and 2. Classify random variables as discrete or continuous.

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Procedure/Learning Experience Activity Complete the following table. The first one is done for you. Experiment Number X Possible Value of X Two cards are drawn from a deck.

Sum of the numbers on the cards

Roll a pair of dice

Sum of the number of dots on the top faces Number of tosses until the coin lands head Height of your father

Toss a pair of coin repeatedly Height of individuals

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4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20

Analysis

This time, you need to reflect on the following questions because it will help you to understand the appropriate way on illustrating and classifying a random variable. Answer the following questions: 1. How do you find the activity/? 2. Where you able to complete the table? If yes, how? If no, why? 3. If a random variable takes on values on continuous scale it is continuous random variable but if a random variable takes on outcomes that are countable then it is discrete random variable. Now, will you be able to classify those experiment as discrete or continuous? If yes, how? If no, why? 4. In your own words how will you differentiate between discrete and continuous random variables?

Abstraction A Random Variable is a numerical quantity that is derived from the outcomes of random experiments. There are two types of random variables, the discrete and continuous random variables

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Types of Random Variables

Discrete

Continuous

A Discrete variable Is a numerical value associated with the desired outcomes? It is also either a finite or infinite number of values but countable such as whole numbers 0,1,2,3.

A Continuous variable Has infinite numerical values associated with any interval on the number line system without any gaps or breaks.

For example: - The number of daily admissions in a hospital - The number of male athletes

For example: - Height - Weight - Skull Circumference

Table 1. Examples of Random Variables Experiment Number X

Possible Values of X

1. Flip a pair of coin 2. Flip a pair of coin repeatedly 3. Set of Integers 4. Set of real numbers

Number of heads in 4 flips of a coin Number of tosses until the coin lands tails Integers from 2 to 6 Real numbers from 2 to 6

0, 1, 2, 3, 4 1, 2, 3, 4, … 2, 3, 4, 5, 6 2...