Lecture 2

Lecture 2 - 1 LECTURE 2. A Working Definition of a Random...

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LECTURE 2. A Working Definition of a Random Variable. If the reader here has read the Preface, then it should be no surprise that this chapter will address the concept of a random variable from a variety of perspectives, ranging from very intuitive, to very mathematical. But, given that the topic of a random variable is usually not addressed until midway into a typical book on statistics, there will be terminology here that, for the moment, may seem vague or incomplete. The reader should have patience. This entire book is devoted to random variables. And it is the purpose of subsequent chapters to clarify things, but in a progressive fashion. The purpose of this chapter is to set the stage, so to speak, for this progression, while at the same time, making the reader feel sufficiently comfortable and enthused to proceed. 1.1 The Concept of a Variable Since for many, a course in statistics seems almost like a course in Spanish or French, it is important to not only begin with clear and precise definitions, but to diminish the requirement that they be memorized. Rather, they should be intuitively appealing, and hence, natural in a conceptual way. To this end, we begin with the notion of a variable . What is a variable? One might say that a variable is something that, simply, can vary , or change. And this is a good start. But, what is meant by a thing? Let’s explore this using some examples. Some Examples of what is a variable, what is not a variable, and what might or might not be a variable. 1. The number 98.6 o F: YES / NO/ MAYBE 2. Your body temperature: YES / NO / MAYBE 3. The act of measuring your body temperature: YES / NO / MAYBE 4. The act of measuring your body temperature to the nearest multiple of 100 o : YES / NO / MAYBE 5. The act of measuring your body temperature to the nearest 0.01 o : YES / NO / MAYBE 6. The act of measuring your body temperature to the nearest 2 o : YES / NO / MAYBE Let’s now draw some conclusions, based on the above answers: C1: C2: C3: 1
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What is Google’s take on the word variable ? var·i·a·ble
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This note was uploaded on 11/01/2009 for the course EE 447 taught by Professor Dontknow during the Spring '09 term at Iowa State.

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Lecture 2 - 1 LECTURE 2. A Working Definition of a Random...

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