Explanation Given Information: The probability density function is defined as f ( x ) = 1 14 over the interval [ 0 , 14 ] . Formula used: Mean: If f is the probability density function f for a continuous random variable x for the interval [ a , b ] , where a and b are real numbers, then the mean of x is defined by the formula, μ = ∫ a b x f ( x ) d x Median: If f is the probability density function f for a continuous random variable x for the interval [ a , b ] , where a and b are real numbers, then the median of x is defined by the formula, ∫ a m f ( x ) d x = 0.5 Calculation: Consider the provided probability density function. f ( x ) = 1 14 over the interval [ 0 , 14 ] Use the formula E ( x ) = ∫ a b x f ( x ) d x for the provided probability density function to calculate the mean. So, E ( x ) = ∫ 0 14 x ⋅ 1 14 d x = 1 14 ∫ 0 14 x d x Use the formula ∫ x n d x = x n + 1 n + 1 and integrate as, 1 14 ∫ 0 14 x d x = 1 14 ( x 2 2

10th Edition

ISBN: 9780357265161

Author: Larson

Publisher: CENGAGE L

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Chapter 9, Problem 45RE

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To calculate: The mean and median of probability density function f(x)=114 over the interval [0,14].

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Chapter 9, Problem 44RE

Chapter 9, Problem 46RE

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The mean and median of probability density function f ( x ) = 1 14 over the interval [ 0 , 14 ] .

Solution Summary: The author calculates the mean and median of the probability density function f(x)=114 over the interval

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To calculate: The mean and median of probability density function f(x)=114 over the interval [0,14].

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Chapter 9 Solutions