Topic: RANDOM VARIABLES AND PROBABILITY DISTRIBUTION MELCs: -illustrate random variable distinguish between a discrete and continuous random variable -find the possible values of a random variable REMEMBER THE FOLLOWING SAMPLE SPACE- the set of all possible outcomes of an experiment Example: a. In throwing a die once, the sample space is S = {1,2,3,4,5,6} b. The sample space of rolling a die and tossing a coin simultaneously is, S = {1H, IT, 2H, 2T, 3H, 3T, 4H, 4T, 5H, 5T, 6H, 6T} c. The sample space of tossing three coins is S = {TTT, TTH, THT, HTT, HHT, HTH, THH, HHH} - RANDOM VARIABLE- is a set of all possible values for a random experiment. It is denoted by a capital letter, usually X,Y and Z. In some random experiments such as: -Tossing coin three times -Rolling a die twice Drawing two balls in a box HOW TO ILLUSTRATE AND GIVE THE VALUE OF RANDOM VARIABLES: Example 1: In a tossing a coin, let X be the random variable denoting the number of tails. Find the value of the random variable X. Using Table of Values, Random Variable Possible Outcomes Possible Values HEAD 0 X=no. of tails TAIL So, the possible values of the random variable X are 0 and 1. Example 2: A coin is tossed 3 times, let X be the random variable denoting the number of heads. Find the values of the random variable X. We can also use Tree Outcomes TTT ITH THT THE HTT HTH HHT HHH Diagram, we can identify X=no. of O 2 3 the outcomes in a given heads Third Toss experiment. Second Toss H HHH First Toss H T HHT H H HTH T T HTT H THH H T THT H TTH TTT Therefore, the possible values of the random variable X are 0,1,2, and 3. TYPES OF RANDOM VARIABLES 1. Discrete Random Variable- is a variable whose value is obtained by counting. Examples: a. The number of students in a class b. The number of test questions answered correctly c. The results or outcomes of rolling a die 2. Continuous Random Variable- is a variable whose value is obtained by measuring. Examples: a. The amount of time required to complete a project. b. The amount of rain, in inches, falls in a storm. c, The height of children. d. The amount of times it takes to sell shoes.Statistics & Probability Topic: RANDOM VARIABLES AND PROBABILITY DISTRIBUTION A. Directions: Write D if the random variable is Discrete and C if it is Continuous. Write your answer on the space provided. 1. The number of defective computers produced by a manufacturer. 2. The speed of a car. 3. The number of siblings in a family of a region. 4. The number of SHS students in a class. 5. The weight of a newborns each year in a hospital. 6. The average amount of electricity consumed for household per month. 7. The time needed to finish the test. 8. The number of voters favoring a candidate. 9. The number of female athletes. 10. The amount of sugar in a cup of coffee. B. Directions. List the sample space of the given experiment. Experiment Sample Space Tossing two coins S = {_ C. Directions. Illustrate and give the value of the random variable of the given problem. A coin is tossed twice. Let Z be the random variable representing the number of heads that occur. Find the values of the random variable Z. Possible Outcomes Value of Random Variable Z So, the possible values of the random variable Z are and