Probability and Statistics Dr. Saeid Moloudzadeh Fundamental Concepts 1 Contents Descriptive Statistics Axioms of Probability Combinatorial Methods Conditional Probability and Independence Distribution Functions and Discrete Random Variables Special Discrete Distributions Continuous Random Variables Special Continuous Distributions Bivariate Distributions

Probability and Statistics Contents Descriptive Statistics Axioms of Probability Combinatorial Methods Conditional Probability and Independence Distribution Functions and Discrete Random Variables Special Discrete Distributions Continuous Random Variables Special Continuous Distributions Bivariate Distributions 2

Chapter 0: Descriptive Statistics Contents 0.1 Fundamental Concepts 0.2 Frequency table and graphs 0.3 Measures of center 0.4 Measures of variation 3

Chapter 0: Descriptive Statistics Contents 0.1 Fundamental Concepts 0.2 Frequency table and graphs 0.3 Measures of center 0.4 Measures of variation 4

Section 1: Fundamental Concepts Definition (Statistics): Statistics is the art of learning from data. It is concerned with the collection of data, their subsequent description and their analysis, which often leads to the drawing of conclusions. There are two subdivisions of statistical method. Definition (Descriptive Statistics): The part of statistics concerned with the description and summarization of data is called descriptive statistics. 5

Section 1: Fundamental Concepts Definition (Inferential Statistics): The part of statistics concerned with the drawing of conclusions from data is called inferential statistics. Definition (Population): The total collection of all the elements (persons or things) that we are interested in is called a population. Definition (Sample): A subgroup of the population that will be studied in detail is called a sample. Definition (Random sample): A sample of k members of a population is said to be a random sample, sometimes called a simple random sample, if the members are chosen in such a way that all possible choices of the k members are equally likely. 6

Section 1: Fundamental Concepts 7

Section 1: Fundamental Concepts Definition (Variable): A characteristic that varies from one person or thing to another in population or sample is called a variable. Examples of variables for humans are height, weight, number of siblings, sex, marital status, and eye color. The first three of these variables yield numerical information and are examples of quantitative variables, last three yield non-numerical information and are examples of qualitative (categorical) variables. Observing the values of the variables for one or more people or things yield data. This value may be a number, a word, or a symbol. The collection of all observations for particular variables is called a data set. 8

Section 1: Fundamental Concepts Qualitative and quantitative variables may be further subdivided : Definition (Nominal Variable): A qualitative variable that categorizes (or describes, or names) an element of a population. Definition (Ordinal Variable): A qualitative variable that incorporates an ordered position, or ranking. 9

Section 1: Fundamental Concepts Definition (Discrete Variable): A quantitative variable that can assume a countable number of values. Intuitively, a discrete variable can assume values corresponding to isolated points along a line interval. That is, there is a gap between any two values. Definition (Continuous Variable): A quantitative variable that can assume an uncountable number of values. Intuitively, a continuous variable can assume any value along a line interval, including every possible value between any two values. 10

Section 1: Fundamental Concepts Example 0.1: A college dean is interested in learning about the average age of faculty. Identify the basic terms in this situation. The population is the age of all faculty members at the college. A sample is any subset of that population. For example, we might select 10 faculty members and determine their age. The variable is the “age” of each faculty member. One data would be the age of a specific faculty member. The data would be the set of values in the sample. 11

Section 1: Fundamental Concepts Example 0.2: Identify each of the following examples as qualitative or quantitative variables. 1. The residence hall for each student in a statistics class. (Qualitative) 2. The amount of gasoline pumped by the next 10 customers at the local Unimart. (Quantitative) 3. The amount of radon in the basement of each of 25 homes in a new development. (Quantitative) 4. The color of the baseball cap worn by each of 20 students. (Qualitative) 5. The length of time to complete a mathematics homework assignment. (Quantitative) 6. The state in which each truck is registered when stopped and inspected at a weigh station. (Qualitative) 12