Chapter 5: Continuous Random Variables PDF

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Chapter 5: Continuous Random Variables pages 232-281 in Statistics textbook by James McClave and Terry Sincich....

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CHAPTER 5 If x follows normal distribution with mean μ and variance 2 x ∼ N (μ , σ ) . If z follows standard normal distribution, it can be denoted as

σ 2 , it can be denoted as ∼ N ( 0,1) .

Note if x follows a continuous distribution, then P ( x =c ) =0 for any real number c , and the following events have the same probability: P ( A < x ≤ b ) =P ( a≤ x < b) =P ( a< x< b )=P ( a ≤ x ≤ b ) P ( a< x )=P ( a ≤ x ) P ( x 0, then P ( z> b) = 0.5− P ( 0< z b ) If 0 < a...