Chapter7 - Chapter 7 Continuous Probability Distributions...

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Chapter 7 Continuous Probability Distributions
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2 Chapter 7: Continuous Probability Distributions 7.1 Continuous Random Variables In Chapter 6, X = In Chapter 7, X = Examples : height, weight, length, length of time, … Example : X = height (male, adult) X is a continuous random variable counting something measuring something This is a continuous random variable This is a discrete random variable
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3 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 6.00000000000000000000001
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4 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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5 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)? Yes, as we will see, but not “=“ probabilities This is 5’ 6”
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6 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’) 3. Chances that a height is between 5.5’ and 6’ is (not zero) Written: P(5.5’ < X < 6’)
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7 Continuous Random Variables Continuous Random Variable A random variable that can take any value over some continuous range of values is called a continuous random variable. Example 7.1.1: Height, weight, length, length of time, etc. They are continuous random variables because they can assume any nonnegative value. We are unable to list all possible values for continuous random variables. Probability statements are concerned with probabilities over a range of values. For examples: The probability that a height is more than 6 ft., that is, P(X ≥ 6´) Chance that a height is between 5.5 ft. and 6 ft., P(5.5´ ≤ X ≤ 6´) To answer these, we need to assume that X = height has a particular shape (i.e., distribution).
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Chapter7 - Chapter 7 Continuous Probability Distributions...

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