tailieunhanh - Lecture Probability & statistics: Chapter 5 - Bùi Dương Hải

Lecture "Probability & statistics - Chapter 5: Discrete probability" has contents: Random variable, probability distribution, expected value, variance – standard deviation, bivariate probability, binomial distribution. | Lecture Probability & statistics: Chapter 5 - Bùi Dương Hải Lecture 5. DISCRETE PROBABILITY Random Variable Probability Distribution Expected value Variance – Standard Deviation Bivariate Probability Binomial Distribution [1] Chapter 5: - 260 PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 1 . Random Variable Random variable: numerical value from a random experiment. Denoted by X, Y, Z, or X1, X2,. Ex. Tossing a die, X is the number of dots - Number of boys in a 3-children family - Score of students’ exam - Temparature during a day - Interest rates in a period of time PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 2 Types of Random Variable Variable , value is random Discrete variable: = ( , , , ) Number of item: = (0, 1, 2, ) Score of test: = (0, 1, 2, , 100) ( = ) is a random event Continuous variable: =( ; ) Time Temperature Length, Weight PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 3 . Discrete Probability Distribution Discrete: = ( , , , ) Denote: = = Value Probability Property: ∑ =1 is discrete probabitily distribution; probabitiy function PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 4 Example Ex. Probability distribution of X, which is the number of Heads when flipping a coin twice Flip a coin twice X = {0, 1, 2} p x 0 1 2 P(x) 1/4 2/4 1/4 Example . Number of Head when flipping a coin 3 times X 0 1 2 3 Probability PROBABILITY & STATISTICS – Bui Duong Hai – NEU – 5 . Parameter Parameter of Random variable: Expected value (Mean) Variance, Standard Deviation Ex. Salary ($) 7 8 9 Frequency 2 5 3 Percent 20% 50% 30% Probability PROBABILITY & STATISTICS – Bui Duong Hai – NEU – .