Explanation Given information: The useful lifetime of a product modelled by the probability density function f ( t ) = 0.16 e − 0.16 t where ‘t’ is the time in years with 0 ≤ t ≤ ∞ . Formula used: If ‘f’ is the probability density function of a continuous random variable x over the interval [ a , b ] , then the expected value or mean is given by; μ = E ( x ) = ∫ a b x f ( x ) d x And, the median ‘x’ is the number m such that; ∫ a m f ( x ) d x = 0.5 The formula for integration by parts is; ∫ u ⋅ v d x = u ∫ v d x − ∫ d u d x [ ∫ v d x ] d x Calculation: Consider given probability density function f ( t ) = 0.16 e − 0.16 t ; 0 ≤ t ≤ ∞ Consider the primary equation μ = E ( t ) = ∫ 0 ∞ t f ( t ) d t = ∫ 0 ∞ t × 0.16 e − 0.16 t d t = 0.16 ∫ 0 ∞ t e − 0.16 t d t Solve by integration by parts ∫ u ⋅ v d x = u ∫ v d x − ∫ d u d x [ ∫ v d x ] d x as here u = x and v = e − 0.16 t therefore; μ = 0.16 ∫ 0 ∞ t e − 0.16 t d t = 0.16 [ t ∫ e − 0

Calculus: An Applied Approach (MindTap Course List)

10th Edition

ISBN: 9781305860919

Author: Ron Larson

Publisher: Cengage Learning

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Chapter 9.3, Problem 40E

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To calculate: The mean and median of the useful life time of a product modelled by the probability density f(t)=0.16e−0.16t function.

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Chapter 9.3, Problem 39E

Chapter 9.3, Problem 41E

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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

Ch. 9.1 - Prob. 5SWU Ch. 9.1 - Prob. 6SWU Ch. 9.1 - Prob. 7SWU Ch. 9.1 - Prob. 8SWU Ch. 9.1 - Prob. 9SWU Ch. 9.1 - Prob. 10SWU Ch. 9.1 - Prob. 1E Ch. 9.1 - Prob. 2E Ch. 9.1 - Prob. 3E Ch. 9.1 - Prob. 4E Ch. 9.1 - Prob. 5E Ch. 9.1 - Prob. 6E Ch. 9.1 - Prob. 7E Ch. 9.1 - Random Selection A card is chosen at random from a...Ch. 9.1 - Prob. 9E Ch. 9.1 - Prob. 10E Ch. 9.1 - Identifying Probability Distributions In Exercises...Ch. 9.1 - Prob. 12E Ch. 9.1 - Prob. 13E Ch. 9.1 - Prob. 14E Ch. 9.1 - Prob. 15E Ch. 9.1 - Using Probability Distributions In Exercises 1518,...Ch. 9.1 - Prob. 17E Ch. 9.1 - Prob. 18E Ch. 9.1 - Prob. 19E Ch. 9.1 - Children The table shows the probability...Ch. 9.1 - Prob. 21E Ch. 9.1 - Die Roll Consider the experiment of rolling a...Ch. 9.1 - Prob. 23E Ch. 9.1 - Prob. 24E Ch. 9.1 - Prob. 25E Ch. 9.1 - Prob. 26E Ch. 9.1 - Prob. 27E Ch. 9.1 - Prob. 28E Ch. 9.1 - Prob. 29E Ch. 9.1 - Personal Income The probability distribution of...Ch. 9.1 - Insurance An insurance company needs to determine...Ch. 9.1 - 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Prob. 21E Ch. 9.2 - Prob. 22E Ch. 9.2 - Prob. 23E Ch. 9.2 - Prob. 24E Ch. 9.2 - Prob. 25E Ch. 9.2 - Finding a Probability In Exercises 19-26, sketch...Ch. 9.2 - Prob. 27E Ch. 9.2 - Prob. 28E Ch. 9.2 - Prob. 29E Ch. 9.2 - Demand The daily demand for gasoline x (in...Ch. 9.2 - Prob. 31E Ch. 9.2 - Prob. 32E Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 34E Ch. 9.2 - Using the Exponential Density Function In...Ch. 9.2 - Prob. 36E Ch. 9.2 - Prob. 37E Ch. 9.2 - Demand The weekly demand x (in tons) for a certain...Ch. 9.2 - Prob. 39E Ch. 9.3 - Prob. 1CP Ch. 9.3 - Find the variance and standard deviation of the...Ch. 9.3 - Use a symbolic integration utility to find the...Ch. 9.3 - Prob. 4CP Ch. 9.3 - Prob. 5CP Ch. 9.3 - Prob. 6CP Ch. 9.3 - Prob. 7CP Ch. 9.3 - Prob. 1SWU Ch. 9.3 - Prob. 2SWU Ch. 9.3 - Prob. 3SWU Ch. 9.3 - Prob. 4SWU Ch. 9.3 - Prob. 5SWU Ch. 9.3 - Prob. 6SWU Ch. 9.3 - Finding Expected Value, Variance, and Standard...Ch. 9.3 - Prob. 2E Ch. 9.3 - Prob. 3E Ch. 9.3 - 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The mean and median of the useful life time of a product modelled by the probability density f ( t ) = 0.16 e − 0.16 t function.

Solution Summary: The author calculates the mean and median of the useful life time of a product modelled by the probability density function.

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To calculate: The mean and median of the useful life time of a product modelled by the probability density f(t)=0.16e−0.16t function.

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Chapter 9 Solutions