Chapter7 - Chapter 7 KVANLI PAVUR KEELING Click to edit...

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Click to edit Master subtitle style 3/13/11 Chapter 7 Continuous Probability Distributions KVANLI PAVUR KEELING
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3/13/11 Chapter Objectives v Keeping thinking about two questions: 1. What is the difference between a discrete distribution and a continuous distribution? ∙ 2. What is normal random
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3/13/11 Continuous Random Variables v In Chapter 6, X = v In Chapter 7, X = v Examples : height, weight, length, length of time, … v Example : X = height (male, adult) v X is a continuous random variable counting somethi ng measuri ng somethi ng This is a continuous random variable This is a discrete random variable
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3/13/11 Continuous Random Variables v 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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3/13/11 P(X=?) = 0 v Is this person’s height exactly 6’? v No - - really close, but not exactly 6’ v What are the chances that a male height is exactly 6’? v Very small - - how small? v In fact, it is zero ! v So, P(X = 6’) is 0
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3/13/11 Continuous Random Variables v How about the chances that a male height is exactly 5.5’? v This is also zero v So, P(X = 5.5’) is 0 v In fact, P(X = any value) is 0 v Does it make sense to talk about probabilities for X = height (any continuous random variable)? v Yes, as we will see, but not “=“ This is 5’ 6”
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3/13/11 Continuous Random Variables v 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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3/13/11 Continuous Random Variables v 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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3/13/11 Continuous Random Variables v 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 v 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’) v Another example: P(5.5’ < X < 6’) is
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3/13/11 Continuous Random Variables v We will assume that male heights (and female heights) follow a bell-shaped curve (normal) v The next slide illustrates the bell- shaped curve for male heights v Central Limit Theorem : When obtaining large samples (generally n>30) from any population, the
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3/13/11 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?
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