Explanation Given Information: The probability density function is defined as f ( x ) = 3 2 − x over the interval [ 0 , 1 ] . 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 is, f ( x ) = 3 2 − x over the interval [ 0 , 1 ] 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 1 x ( 3 2 − x ) d x = ∫ 0 1 x ( 3 2 − 2 x 2 ) d x = 1 2 ∫ 0 1 ( 3 x − 2 x 2 ) d x Use the formula ∫ x n d x = x n + 1 n + 1 and integrate as, 1 2 ∫ 0 1 ( 3 x − 2 x 2 ) d x = 1 2 ( 3 x 2 2 − 2 x 3 3 ) 0 1 Use the Fundamental theorem ∫ a b f ( x ) d x = F ( b ) − F ( a ) and apply the limits as, 1 2 ( 3 x 2 2 − 2 x 3 3 ) 0 1 = 1 2 [ ( 3 ( 1 2 ) 2 − 2<

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 9, Problem 46RE

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To calculate: The mean and median of probability density function f(x)=32−x over the interval [0,1].

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Chapter 9, Problem 45RE

Chapter 9, Problem 47RE

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Chapter 9 Solutions

Calculus: An Applied Approach (MindTap Course List)

Ch. 9.1 - Checkpoint 1 Worked-out solution available at...Ch. 9.1 - Prob. 2CP Ch. 9.1 - Prob. 3CP Ch. 9.1 - Prob. 4CP Ch. 9.1 - Prob. 5CP Ch. 9.1 - Prob. 6CP Ch. 9.1 - Prob. 1SWU Ch. 9.1 - Prob. 2SWU Ch. 9.1 - Prob. 3SWU Ch. 9.1 - Prob. 4SWU

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The mean and median of probability density function f ( x ) = 3 2 − x over the interval [ 0 , 1 ] .

Solution Summary: The author calculates the mean and median of the probability density function f(x)=32-x over the interval.

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To calculate: The mean and median of probability density function f(x)=32−x over the interval [0,1].

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Chapter 9 Solutions