Stat400Lec12(Ch3.6,10.5)

# Stat400Lec12(Ch3.6,10.5) - STAT 400 Lecture 12 Q-Q Plot...

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STAT 400 Lecture 12 Chapter 3.6, 10.5 Spring 2012 Q-Q Plot.

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Markov’s Inequality: Let u ( X ) be a non-negative function of the random variable X. If E [ u ( X ) ] exists, then, for every positive constant c , P ( u ( X ) c ) ( ) [ ] c u X E . Chebyshev’s Inequality: Let X be any random variable with mean µ and variance σ 2 . For any ε > 0, P ( | X – µ | ε ) 2 2 ε σ or, equivalently, P ( | X – µ | < ε ) 2 2 ε σ 1 Setting ε = k σ , k > 1, we obtain P ( | X – µ | k σ ) 2 1 k or, equivalently, P ( | X – µ | < k σ ) 2 1 1 k That is, for any k > 1, the probability that the value of any random variable will be within k standard deviations of its mean is at least 2 1 1 k . Example 1 : Suppose µ = E ( X ) = 17, σ = SD ( X ) = 5. Consider interval ( 9, 25 ) = ( 17 – 8, 17 + 8 ). k = 5 8 = 1.6. P ( 9 < X < 25 ) = P ( | X – µ | < 1.6 σ ) 2 6 . 1 1 1 = 0.609375 .
Example 2 Suppose also that the distribution of

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Stat400Lec12(Ch3.6,10.5) - STAT 400 Lecture 12 Q-Q Plot...

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