Math 135 Week 12 Lecture Notes Bittenger 10th

# Example 2 given the probability density function f x

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Unformatted text preview: ensity function for x defined over [ a, b ] . Variance and Standard Deviation DEFINITION: The variance, σ 2 , of a continuous random variable x, is defined on [ a, b ] , with probability density function f, is σ 2 = E ( x2 ) − µ2 = E ( x 2 ) − ⎡ E ( x )⎤ ⎣ ⎦ 2 2 b b = ∫ x 2 f ( x ) dx − ⎡ ∫ xf ( x ) dx ⎤ ⎢ ⎥ a ⎣a ⎦ The standard deviation, σ , of a continuous random variable is defined as σ = variance . Example 2: Given the probability density function f ( x ) = 1 − 1 x , over [ 0, 4 ] , find the mean, the 2 8 variance, and the standard deviation. Math 135 Class Notes – Week 12 Bittenger 10th Ed. 7 The Normal Distribution DEFINITION: A continuous random variable x has a standard normal distribution if its probability density function is f ( x) = 1 − x22 e , over ( −∞, ∞ ) 2π DEFINITION: A continuous random variable x is normally distributed with mean µ and standard deviation σ if its probability density function is given by f ( x) = 2 1 − 1 ⎡( x − µ )/σ ⎤ ⎦ e ( 2 )⎣ , over ( −∞, ∞ ) σ 2π...
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## This document was uploaded on 02/19/2014 for the course MATH 135 at CSU Chico.

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