351notesSu081.1-1.2

# 351notesSu081.1-1.2 - WELCOME TO STT 351 PROBABILITY AND...

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WELCOME TO STT 351 PROBABILITY AND STATISTICS FOR ENGINEERS INSTRUCTOR: ELIJAH E. DIKONG 1.1 INTRODUCTION WHY STATISTICS? IT IS THE SCIENCE THAT HELPS TO UNDERSTAND MANY PHENOMENA WHICH OCCUR IN YOUR FIELD OF ENGINEERING OR SCIENCE. IT IS THE SCIENTIFIC WAY THAT HELPS TO MAKE INTELLIGENT JUDGEMENTS OR DECISIONS IN THE PRESENCE OF UNCERTAINTY AND VARIATION. 1

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CONSIDER THE FOLLOWING TWO EXAMPLES Example 1: Emission levels of a vehicle: HC (gm/mile): 12.8, 18.3, 32.2, 32.5 CO (gm/mile): 118, 149, 232, 236 WHAT IS THE CO LEVEL? Difficult to make a statement, as there is a high variation. Example 2: Marks of two students in 4 tests: S1: 25, 38, 42, 39 S2: 85, 62, 78, 59 WHO IS DOING BETTER? WHERE THERE IS NO DIFFICULTY IN ANSWERING, THERE IS NO NEED FOR STATISTICAL ANALYSIS. 2
WHAT IS STATISTICS? ONE WORD DEFINITION: (a) ECONOMICS: Money (b) PHILOSOPHY: Why (c) STATISTICS: VARIATION LAYMAN DEFINITION: INFORMATION OR SUMMARY OF DATA. FORMAL DEFINITION: Statistics deals with techniques to (a) obtain information /data (sample), (b) analyze scientifically the data collected, (c) draw valid conclusions or inferences SOME TERMINOLOGIES POPULATION: A SET OF A WELL-DEFINED COLLECTION OF OBJECTS OR ELEMENTS OF INTEREST WHICH ARE UNDER INVESTIGATION. THE STUDENTS STUDYING ENGINEERING IN MSU. THE POPULATION OF EAST LANSING. 3

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IF WE COLLECT INFORMATION ON ALL THE ELEMENTS IN THE POPULATION, WE CALL IT CENSUS .’ [MOST OFTEN, THIS IS IMPOSSIBLE] SAMPLE : A SUBSET OF A POPULATION, WHICH IS SELECTED IN SOME PRESCRIBED MANNER FOR OBTAINING INFORMATION. Often, we are interested in certain CHARACTERISTICS of the population (number of flaws in a piece of cloth; thickness of a capsule wall, monthly income of an individual etc). A characteristic may be (i) Categorical or Qualitative i.e. belongs to one of the categories, such as Gender of a student (male/female); Quality of a product (excellent / good / bad) (ii) Numerical or Quantitative i.e. measured in real value. For example, (a) heights of students, (b) values of a stock. 4
A variable is any characteristic whose value may change from one object to another in the population. NOTATION : Lowercase letters of the English alphabet e.g. x, y, z are usually used. A variable x may be categorical called categorical variable or quantitative called quantitative variable . TYPES OF DATA (i) The data x 1 …… x n on a categorical variable x is called categorical data. (ii) The data x 1 …… x n on a numerical variable x is called quantitative data. DEFINITION : A UNIVARIATE DATA SET CONSISTS OF OBSERVATIONS ON A SINGLE VARIABLE. Example : Type of transmission, automatic A or manual M, on each of ten automobiles recently purchased at a certain dealership. M

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## This note was uploaded on 07/25/2008 for the course STT 351 taught by Professor Palaniappan during the Summer '08 term at Michigan State University.

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351notesSu081.1-1.2 - WELCOME TO STT 351 PROBABILITY AND...

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