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.Direction: Read each item carefully. Choose the letter of the correct answer then write it on the blank provided. 1. It is a set of possible values for a random experiment. a. sample space b. Random variable c. Set d. sample 2. The following random variables are discrete, EXCEPT. 15.0 - (22X21 a. The number of defective computers produced by a manufacturer in a certain school. b. The number of siblings in a family of a region. . c. The speed of a car. d. The number of female athletes of the Sports track. 0e.0 = (01 2 X 2 0)1.0 er.0 = (012728)9.0 3. It is a variable whose value is obtained by measuring. a. Continuous Random Variable erit to zevi c. Random Variable b. Discrete Random Variable sonohov d. Sample Space 4.If two coins are tossed, which is not possible value of the random variable for the number of heads? a. 0 Searli to llo . b b. 1 C. 2 . bobnote brio d. 3 5. If two coins are tossed, which of the following is the sample space? a. S = {TT, TH, HH, HT} odoly silt of ister . 81:5/ medmuni b. S = {TT, TH} Snoitudialb villidodong ort to noem sift al forW .NI. (X)9 C. S = {TTT, THT, HHT, HHH} S.I .d d. S = {TTT, HHH} 8.1 .6 6. Which of the following is NOT a true statement? a. The value of a random variable could be zero. idodong ert to sonphov ertal tow .81. b. Random variables can only have one value. 25.0 .0 The probability of the value of a random variable could be zero. d. The sum of all the probabilities in a probability distribution is always equal to one. 7. Which formula gives the probability distribution shown by the table? X 3 6 It al fonw er IS.O . P(X) NIH 6 SS-OR aredmun Spoiludhiziby a. P(x ) = = b. P(x) = C. P(x) = 5 d. P(x) = 1 (X)9 O.S . d 8. If P(x) = =, what are the possible values of x for it to be a probability distribution? a. 0, 2, 3 b. 1, 2, 3 C. 2, 3, 4 d. 1, 1, 2 villidodong ant to gononov or! 9. The following represents a probability distribution, EXCEPT. 2.4.0 a. P(1) = 0.08 , P(2) = 0.12 , P(3) = 1.03 28.3.0 b. P(1) = 0.42 , P(2) = 0.31 , P(3) = 0.27 00.8 .5 C. P(1) = = , P(2) = 2 , P(3) = - d. P(1) = 0 , P(2) = 0.71 , P(3) = 0.29 10. Which of the following represents a probability distribution? I to noitoiveb bobnote ent a lonwiss. E8.S. X 3 5 7 D C. P(1) = 0.42 , P(2) = 0.31 , P(3) = 0.37 P(X) 0.35 0.25 0.22 0.12 . wolad n Snoltucklab villidodong orit to noem e b. 0 2 6 8 P(X) d. P(1) = 0.08 , P(2) = 0.12 , P(3) = 1.03For numbers 1 1-14, refer to the table below. The following data show the probabilities for the number of cars sold in a given day at a car dealer store. _11. Find P(x 5 2) No of cars X Probability P (X) YAHIA 70 3017TO KORIVIG 230 a. P(x 5 2) = 2.00 JOOHOZ HOUR JAMOITAN WAR 0 0.100 b. P(x 5 2) = 0.5 0.150 C. P(x 5 2) = 3.5 2 0.250 d. P(x a) b. P(z