Introduction to Probability Theory, Schemes and Mind Maps of Statistics

Download Introduction to Probability Theory and more Schemes and Mind Maps Statistics in PDF only on Docsity! Probability Theory for lecturer mathematics 0301-4889903 Lec#02  Some basic terminologies  Sample Space 0301-4889903 ALI RAZA 2 Experiment: Any process of observations is called experiment. Outcomes: The result of an observation are known as outcomes of an experiment. Random Experiment: An experiment is called a random experiment if its outcomes cannot be predicted. So a random experiment is an experiment which produces different outcomes even if it is repeated a large number of times under similar conditions. Examples: 1) Rolling a die. 2) Tossing a coin. 3) Drawing a card from a deck. 4) Choosing a ball from a bag containing balls of different colors. Sample Space: The set of all possible outcomes of a random experiment is called sample space. Denoted by S. An element of S is called a sample point. Lec#01 Probability Theory | Lecturer Mathematics preparation 0301-4889903 ALI RAZA 5 4) In rolling a die. Sample space is given by (61 = 6) 5) In rolling two dice. Sample space is given by (62 = 36) Lec#01 Probability Theory | Lecturer Mathematics preparation 𝑆 = {1, 2, 3, 4, 5, 6} 𝑆 = { (1, 1), (1, 2), (1,3 ), (1, 4), (1, 5), 1, 6 , 2, 1 , 2, 2 , 2,3 , 2,4 , (2,5), 2,6 , 3,1 , 3,2 , 3,3 , 3, 4 , 3,5 , 3,6 , 4,1 , 4,2 , 4,3 , 4,4 , 4,5 , 4,6 , 5,1 , 5,2 , 5,3 , 5,4 , 5,5 , 5,6 , (6,1), (6,2), (6,3), (6,4), (6,5), 6,6 } 0301-4889903 ALI RAZA 6 6) In the experiment of drawing card from an ordinary deck of cards. Sample space consists of 52 elements. Lec#01 Probability Theory | Lecturer Mathematics preparation 0301-4889903 ALI RAZA 7 Lec#01 Probability Theory | Lecturer Mathematics preparation CLUB HEART SPADE DIAMONDS ACE Cards KINGS QUEENS JACKS