Random Variables and Probability Distributions PDF

RANDOM VARIABLES & PROBABILITY DISTRIBUTIONS CHAPTER 1 REVIEW! STATISTICS -is a branch of mathematics that deals with collection, organization, presentation, analysis and interpretation of data.  Two Major Areas of Statistics DESCRIP...

RANDOM VARIABLES & PROBABILITY DISTRIBUTIONS CHAPTER 1 REVIEW! STATISTICS -is a branch of mathematics that deals with collection, organization, presentation, analysis and interpretation of data.  Two Major Areas of Statistics DESCRIPTIVE STATISTICS a statistical method concerned with describing, showing, summarizing the properties and characteristics of a set of data. INFERENTIAL STATISTICS a statistical method concerned using measurements from the sample subjects in the experiment to compare the treatment groups and make generalizations about the larger population of subjects. PROBABILITY is a branch of mathematics that deals with the chance of an event occurring. SAMPLE SPACE set of all possible outcomes in an experiment. EVENT the situation in which a desired outcome occurs. It is a subset of the sample space. LESSON 1 RANDOM VARIABLES  Learning Outcomes I.1. Illustrates a random variable (discrete and continuous). I.2. distinguishes between a discrete and a continuous random variable. I.3. finds the possible values of a random variable. RANDOM - chosen, done without a particular plan or pattern Ex: drawing raffle tickets or names from a bowl VARIABLES - A quantity that can have any one of a set of values or a symbol that represents such a quantity. It is always represent in capital letter Y. Ex: age, civil, status, X, Y, Z  RANDOM VARIABLE - value depends on the outcome of a random process. - a variable whose value is 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.  Two Kinds of Random Variable DISCRETE RANDOM VARIABLE CONTINUOUS RANDOM VARIABLE A random variable that take an A random variable that can take infinitely uncountable number of on a finite (countably infinite/ possible values, typically countable/count data) number of measurable quantities. distinct values. A random variable that measured About whole numbers. data (time, distance, amount).  DISCRETE RANDOM VARIABLE Examples: 1. Number of heads obtained when tossing a coin thrice. 2. The number of siblings a person has. 3. The number of student’s present in a classroom at a given time.  CONTINUOUS RANDOM VARIABLE Examples: 1. time of person can hold his/her breath. 2. the height/weight of a person. 3. body temperature.  Classify each random variable as DISCRETE or CONTINUOUS Examples: 1. Score of a student in a quiz. 2. How long students ate breakfast. 3. Time to finish running 100m. 4. Amount of paint utilized in a building project. 5. The number of deaths per year attributed to lung cancer. 6. The speed of a car.  Classify each random variable as DISCRETE or CONTINUOUS Examples: 7. The number of dropout in a school district for a period of 10 years. 8. The number of voters favoring a candidate. 9. The time needed to finish the test. 10. Number of eggs a hen lays. 11. Average temperature in Baguio City for the past 5 days. 12. Weights of 8 randomly Math books.  Classify each random variable as DISCRETE or CONTINUOUS Examples: 13. Amount of sugar in a cup of coffee. 14. Amount of rainfall (in mm) in different cities in NCR. 15. Number of gifts received by 20 students during Christmas season.  Example 1: Suppose two coins are tossed. Let X be the random variable representing the number of heads that occur. Find the values of the random variable X. Sample Space = {HH, HT, TH, TT} POSSIBLE OUTCOMES VALUE OF RANDOM VARIABLE X (number of heads) HH 2 HT 1 TH 1 TT 0 So the possible values of the random variable X are 0, 1, and 2. X = {0,1,2}  Example 2: 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. POSSIBLE VALUE OF RANDOM VARIABLE Y (number of OUTCOMES tails) HHH 0 HHT 1 HTH 1 HTT 2 THH 1 THT 2 Sample Space = {HHH, HHT, HTH, TTH 2 HTT, THH, THT, TTH, TTT} TTT 3 Y = {0,1,2,3}  Example 3: Suppose three cellphones are tested at random. Let X be the random variable representing the number of defective cellphones that occur. Find then values of the random variable X. VALUE OF RANDOM D = Defective cp POSSIBLE VARIABLE Z (number of OUTCOMES B = Not defective cp blue balls) DDD 3 DDN 2 Sample Space = {DDD, DDN, DND, DND 2 DNN, NDD, NDN, NND, NNN} DNN 1 NDD 2 NDN 1 X = {0,1,2,3} NND 1 NNN 0 Let’s try ! Write all the possible values of each random variable. 1. X: Number or even number outcomes in a roll of a die. 2. Y: scores of a student in a 10-item test. 3. Z: Product of two numbers taken from two boxes containing numbers 0 to 3. Let’s try ! Write all the possible values of each random variable. 1. X: Number or even number outcomes in a roll of a die. 2. Y: scores of a student in a 10-item test. 3. Z: Product of two numbers taken from two boxes containing numbers 0 to 3.