Chapter 7 - Click to edit Master subtitle style Chapter 7...

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Click to edit Master subtitle style 3/10/11 Chapter 7 Continuous Probability Distributions KVANLI PAVUR KEELING
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3/10/11 Chapter Objectives At the completion of this chapter, you should be able to: Distinguish between a discrete distribution and a
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3/10/11 Continuous Random Variables In Chapter 6, X = In Chapter 7, X = Examples : height, weight, length, length of time, … Example : X = height (male, adult) counting somethi ng measuri ng somethi ng This is a continuous random variable This is a discrete random variable
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3/10/11 Continuous Random Variables What are the chances X is exactly 6’? Claims he is exactly 6’ Suppose we have a measuring device that can measure heights to any number of decimal places It turns out that his height is 6.000000000000000000000 00001
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3/10/11 Continuous Random Variables Is this person’s height exactly 6’? No - - really close, but not exactly 6’ What are the chances that a male height is exactly 6’? Very small - - how small? In fact, it is zero! So, P(X = 6’) is 0
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3/10/11 Continuous Random Variables How about the chances that a male height is exactly 5.5’? This is also zero So, P(X = 5.5’) is 0 In fact, P(X = any value) is 0 Does it make sense to talk about probabilities for X = height (any continuous random variable)? This is 5’ 6”
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3/10/11 Continuous Random Variables In Chapter 6, we could list the values of X __ with probability __ with probability X = __ with probability __ with probability __ with probability
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3/10/11 Continuous Random Variables We can find these probabilities: 1. Chances that a height is more than 6’ is (not zero) Written: P(X > 6’) 2. Chances that a height is less than 5.5’ is (not zero) Written: P(X < 5.5’)
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3/10/11 Continuous Random Variables A nice thing in this chapter (any continuous random variable) is that you need not worry about whether you should include the equal sign, “=“, in your inequalities For example, P(X > 6’) is the same as P(X ≥ 6’) since P(X = 6’) is zero and P(X > 6’) is the same as P(X ≥ 6’) Another example: P(5.5’ < X < 6’) is
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3/10/11 Continuous Random Variables To discuss probabilities and determine the previous three probabilities concerning height, we need to assume that X = height has a particular shape We will assume that male heights (and female heights) follow a bell- shaped curve
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3/10/11 Bell-Shaped Curve for Male Heights X = ht. Point where the curve changes shape – called an inflection point It turns out that this is the standard deviation of X Symbol: σ (sigma) We’ll assume σ = .25’ (3”) Need to know: 1. Where is the middle? 2. How wide is it? µ = 5.75’
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3/10/11 A Closer Look at the Height Curve X = Ht. . 25 6’ 6.25’ 6.5’ This is 5.75’ + .25’ = 6’ 5.5’ .
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This note was uploaded on 03/09/2011 for the course DSCI 2710 taught by Professor Hossain during the Fall '08 term at North Texas.

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Chapter 7 - Click to edit Master subtitle style Chapter 7...

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