STATISTICS AND PROBABILITY DISTRIBUTIONS
- 2. CHAPTER 1: RANDOM VARIABLES AND PROBABILITY DISTRIBUTION LESSON 1: EXPLORING RANDOM VARIABLES LESSON 2: CONSTRUCTING PROBABILITY DISTRIBUTION LESSON 3: COMPUTING THE MEAN OF A DISCRETE PROBABILITY LESSON 4: COMPUTING THE VARIANCE OF A DISCRETE PROBABILITY DISTRIBUTION
- 3. LESSON 1: EXPLORING RANDOM VARIABLES AFTER GOING THROUGH THIS LESSON, YOU ARE EXPECTED TO 1. DEFINE RANDOM VARIABLE; AND 2. ILLUSTRATE RANDOM VARIABLES (DISCRETE AND CONTINUOUS).
- 4. UNLOCKING TERMS EXPERIMENT- ANY MOVEMENT THAT SHOULD BE POSSIBLE MORE THAN ONCE UNDER COMPARATIVE CONDITION. EX: TOSSING A COIN SAMPLE SPACE- THE ARRANGEMENT OF EVERY POSSIBLE OUTCOMES OF AN EXPERIMENT. EX:(HEAD, TAIL) RANDOM- CHOSEN, DONE WITHOUT A PARTICULAR PLAN OR PATTERN. EX: DRAWING RAFFLE TICKETS OR NAMES FROM A BOWL VARIABLE- A QUANTITY THAT CAN HAVE ANY ONE OF A SET OF VALUES OR A SYMBOL THAT REPRESENTS SUCH A QUANTITY. EX: AGE, CIVIL STATUS, X, Y, Z
- 5. RANDOMVARIABLE • VALUE DEPENDS ON THE OUTCOMES OF A RANDOM PROCESS. • A VARIABLE WHOSE VALUE IS A NUMERICAL OUTCOME OF A RANDOM PHENOMENON. • DENOTED WITH A CAPITAL LETTER. • DISCRETE OR CONTINUOUS. EX: NUMBER OF HEADS, NUMBER OF TAILS, NUMBER OF BOYS IN THE FAMILY.
- 6. DISCRETE RANDOMVARIABLE • A VARIABLE THAT CAN TAKE ON A FINITE NUMBER OF DISTINCT VALUES
- 7. CONTINUOUS RANDOM VARIABLE • A RANDOM VARIABLE THAT CAN TAKE AN INTERMINABLY UNCOUNTABLE NUMBER OF POTENTIAL VALUES, REGULARLY MEASURABLY AMOUNTS.
- 8. EXAMPLE 1: TOSSING A COIN TOSS YOUR ONE-PESO COIN THREE TIMES AND RECORD IN YOUR NOTEBOOK THE RESULTS OF THE THREE TOSSES. IN ORDER TO WRITE THE RESULT EASILY, USE LETTER H FOR THE HEADS AND LETTER T FOR THE TAILS.
- 9. TOSSING A COIN EXPERIMENT SAMPLE SPACE TOSSING A COIN THREE TIMES {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH}
- 10. TOSSING A COIN SAMPLE SPACE NUMBER OF HEADS (X) TTT 0 THT 1 TTH 1 HTT 1 HTH 2 THH 2 HHT 2 HHH 3
- 11. EXAMPLES OF RANDOM VARIABLES EXPERIMENT NUMBER X OR THE RANDOM VARIABLE X TYPES OF RANDOM VARIABLE 1. RECORD THE NUMBER OF HOURS A SPECIFIC STUDENT USE THEIR MOBILE FROM 8:00 AM TO 5:00 PM FOR THE PAST THREE NIGHTS THE NUMBER OF HOURS A SPECIFIC STUDENT USE THEIR MOBILE FROM 8:00 AM TO 5:00 PM DISCRETE 2. BUYING TWO TRAYS OF EGG IN THE MARKET THE WEIGHT OF EGGS IN KILOGRAMS CONTINUOUS 3. RECORDING OF THE GENDER OF FAMILY WITH THREE CHILDREN THE NUMBER OF BOYS AMONG THE CHILDREN DISCRETE 4. STUDENTS WILL PREPARE FOR A QUIZ IN MATHEMATICS HOW MUCH TIME SPENDS REVIEWING FOR THIS QUIZ CONTINUOUS 5. ROLLING A PAIR OF DICE NUMBERS APPEARED IN A PAIR OF DICE DISCRETE
- 12. ASSESSMENT COMPLETE THE TABLE BELOW AND IDENTIFY THE RANDOM VARIABLE IN THE GIVEN EXPERIMENT. TELL WHAT TYPE OF RANDOM VARIABLE IT IS. EXPERIMENT RANDOM VARIABLE TYPES OF RANDOM VARIABLE 1. LISTING THE SEX OF FAMILY MEMBERS WITH 4 CHILDREN THE NUMBER OF BOYS AND NUMBER OF GIRLS IN THE FAMILY DISCRETE (NUMBER OF BOYS AND GIRLS ARE COUNTABLE) 2. THE TEACHER GIVES A 50- ITEM MULTIPLE CHOICE TEST THE TIME A STUDENT FINISHES THE TEST CONTINUOUS (THE TIME GIVEN IS NOT A WHOLE NUMBER) 3. RECORDING THE NUMBER OF COVID-19 PATIENTS IN A DAY IN DIFFERENT HOSPITAL 4. WEIGHT OF PERSONS WORKING OUT IN THE GYM
- 13. EXPERIMENT RANDOM VARIABLES TYPES OF RANDOM VARIABLE 5. AVERAGE MOBILE DATA CONSUMPTION OF STUDENTS ATTENDING ONLINE CLASS 6. THE NUMBER OF TEXT MESSAGES SENT IN A DAY OF A SUBSCRIBER 7. AVERAGE NUMBER OF PERSONS VIOLATING QUARANTINE PROTOCOLS 8. ROLLING TWO DICE 9. RECORD THE NUMBER OF HOURS ONE SURF THE INTERNET FROM 5 PM TO 10 PM FOR THE PAST FIVE NIGHTS 10. RUN TIMES OF A RUNNER FOR RUNNING 100 M ON THE TRACK
- 14. GUIDE QUESTIONS • HOW DID YOU FIND THE RANDOM VARIABLE? ILLUSTRATE. • FROM YOUR ANSWERS IN THE TABLE ABOVE, WHICH EXPERIMENTS ARE DISCRETE? WHICH EXPERIMENTS ARE CONTINUOUS?
- 15. ASSESSMENT COMPLETE THE FOLLOWING STATEMENTS BY WRITING THE CORRECT WORD. 1. THE SET OF THE POSSIBLE OUTCOMES OF AN EXPERIMENT IS CALLED__________. 2. A VARIABLE WHOSE VALUE IS OBTAINED BY MEASURING IS CALLED_____________. 3. A VARIABLE THAT CAN BE DISCRETE OR CONTINUOUS IS___________. 4. TIME IT TAKES TO FINISH THE TEST IS AN EXAMPLE OF___________. 5. GETTING A 1 IN ROLLING A DIE IS AN EXAMPLE OF_____________.
- 16. ANSWER THE FOLLOWING. CLASSIFY WHETHER THE GIVEN EXPERIMENTS IMPLIES A DISCRETE RANDOM VARIABLE OR A CONTINUOUS RANDOM VARIABLE. _______1. THE AVERAGE NUMBER OF PATIENTS IN A HOSPITAL FOR A WEEK. _______2. COLLECTING DATA ABOUT THE WEIGHTS OF NEWBORNS IN A LYING-IN CLINIC. _______3. RECORDING THE DISTANCE TRAVELLED BY THE LEMERY-SARA JEEPNEY. _______4. LISTING THE NUMBER OF CASES DUE TO COVID-19 IN ILOILO CITY. _______5. NUMBER OF STUDENTS ATTENDING ONLINE CLASS.