Explanation Definition used: “A probability density function of a random variable X in an interval I , where I may be bounded or unbounded, is a nonnegative function f having the following properties. 1. The total area of the region under the graph of f is equal to 1 2. The probability that an observed value of the random variable X lies in the interval [ a , b ] is P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x .” Proof: The function f ( x ) is a probability density function if it satisfies the above two properties. Check the function f ( x ) is non-negative in the interval [ 0 , 3 ] or not. Substitute x = 0 in 1 9 ( x 9 − x 2 ) as follows. f ( 0 ) = 1 9 ( ( 0 ) 9 − ( 0 ) 2 ) = 1 9 ( 0 ) = 0 Substitute x = 3 in 1 9 ( x 9 − x 2 ) . f ( 3 ) = 1 9 ( ( 3 ) 9 − ( 3 ) 2 ) = 1 9 ( 3 9 − 9 ) = 1 9 ( 0 ) = 0 Therefore 1 9 ( x 9 − x 2 ) = 0 for all values of x in the interval [ 0 , 3 ] the function f ( x ) is non-negative. Thus, the function f ( x ) = 1 9 ( x 9 − x 2 ) is non-negative on the interval [ 0 , 3 ] . Check the area of the region under the graph of f ( x ) is equal to 1 or not. Integrate the function f ( x ) on the interval [ 0 , 3 ] and obtain the area. That is, ∫ 0 3 ( 1 9 ( x 9 − x 2 ) ) d x

Bundle: Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach, 10th + WebAssign Printed Access Card for Tan's Applied ... A Brief Approach, 10th Edition, Single-Term

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ISBN: 9781305139824

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 7, Problem 27RE

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To show: The function f(x)=19(x9−x2) is a probability density function on the interval [0,3] .

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Chapter 7, Problem 26RE

Chapter 7, Problem 28RE

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Chapter 7 Solutions

Bundle: Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach, 10th + WebAssign Printed Access Card for Tan's Applied ... A Brief Approach, 10th Edition, Single-Term

Ch. 7.1 - Write the formula for integration by parts.Ch. 7.1 - Explain how you would choose u and dv when using...Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 2E Ch. 7.1 - Prob. 3E Ch. 7.1 - Prob. 4E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 6E Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E

Ch. 7.1 - Prob. 9E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 11E Ch. 7.1 - Prob. 12E Ch. 7.1 - Prob. 13E Ch. 7.1 - Prob. 14E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 16E Ch. 7.1 - Prob. 17E Ch. 7.1 - Prob. 18E Ch. 7.1 - Prob. 19E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 22E Ch. 7.1 - Prob. 23E Ch. 7.1 - Prob. 24E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 26E Ch. 7.1 - In Exercises 1-26, find each indefinite integral....Ch. 7.1 - Prob. 28E Ch. 7.1 - Prob. 29E Ch. 7.1 - In Exercises 29-34, evaluate each definite...Ch. 7.1 - Prob. 31E Ch. 7.1 - Prob. 32E Ch. 7.1 - Prob. 33E Ch. 7.1 - Prob. 34E Ch. 7.1 - Find the function f given that the slope of the...Ch. 7.1 - Prob. 36E Ch. 7.1 - Prob. 37E Ch. 7.1 - Prob. 38E Ch. 7.1 - Prob. 39E Ch. 7.1 - Production of Steam Coal In keeping with the...Ch. 7.1 - Prob. 41E Ch. 7.1 - Concentration of a Drug in the Bloodstream The...Ch. 7.1 - Prob. 43E Ch. 7.1 - Average price of a Commodity The price of a...Ch. 7.1 - Distance Covered by a Car The velocity of the...Ch. 7.1 - Credit Card Losses in the United Kingdom The mail...Ch. 7.1 - U.S. Smartphone Users Smartphone users, as a...Ch. 7.1 - Prob. 49E Ch. 7.1 - Future Value of AN Investment Laura, the sole...Ch. 7.1 - Rate of Return on an Investment Suppose an...Ch. 7.1 - Present Value of A Franchise Tracy purchased a...Ch. 7.1 - Gini Index Refer to Section 6.7. The income...Ch. 7.1 - Prob. 56E Ch. 7.1 - A Mixture Problem Two tanks are connected in...Ch. 7.1 - Prob. 58E Ch. 7.1 - Prob. 59E Ch. 7.1 - In Exercises 59-62, determine whether the...Ch. 7.1 - In Exercises 59-62, determine whether the...Ch. 7.1 - Prob. 62E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 5E Ch. 7.2 - Prob. 6E Ch. 7.2 - Prob. 7E Ch. 7.2 - Prob. 8E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 10E Ch. 7.2 - Prob. 11E Ch. 7.2 - Prob. 12E Ch. 7.2 - Prob. 13E Ch. 7.2 - Prob. 14E Ch. 7.2 - Prob. 15E Ch. 7.2 - Prob. 16E Ch. 7.2 - Prob. 17E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 19E Ch. 7.2 - Prob. 20E Ch. 7.2 - Prob. 21E Ch. 7.2 - Prob. 22E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 24E Ch. 7.2 - Prob. 25E Ch. 7.2 - In Exercises 1-32, use the table of integrals in...Ch. 7.2 - Prob. 27E Ch. 7.2 - Prob. 28E Ch. 7.2 - Prob. 29E Ch. 7.2 - Prob. 30E Ch. 7.2 - Prob. 31E Ch. 7.2 - Prob. 32E Ch. 7.2 - Prob. 33E Ch. 7.2 - Prob. 34E Ch. 7.2 - Prob. 35E Ch. 7.2 - Prob. 36E Ch. 7.2 - Prob. 37E Ch. 7.2 - Prob. 38E Ch. 7.2 - Producers' SURPLUS for WOMEN'S Boots Refer to...Ch. 7.2 - Prob. 40E Ch. 7.2 - Prob. 41E Ch. 7.2 - Prob. 42E Ch. 7.2 - Prob. 43E Ch. 7.2 - Prob. 44E Ch. 7.2 - Prob. 45E Ch. 7.2 - Prob. 46E Ch. 7.2 - Prob. 47E Ch. 7.3 - Explain why n can be odd or even in the...Ch. 7.3 - Prob. 1E Ch. 7.3 - Prob. 2E Ch. 7.3 - Prob. 3E Ch. 7.3 - Prob. 4E Ch. 7.3 - Prob. 5E Ch. 7.3 - Prob. 6E Ch. 7.3 - Prob. 7E Ch. 7.3 - Prob. 8E Ch. 7.3 - Prob. 9E Ch. 7.3 - In Exercises 114, use the Trapezoidal Rule and...Ch. 7.3 - Prob. 11E Ch. 7.3 - Prob. 12E Ch. 7.3 - Prob. 13E Ch. 7.3 - Prob. 14E Ch. 7.3 - Prob. 15E Ch. 7.3 - Prob. 16E Ch. 7.3 - Prob. 17E Ch. 7.3 - Prob. 18E Ch. 7.3 - Prob. 19E Ch. 7.3 - Prob. 20E Ch. 7.3 - Prob. 21E Ch. 7.3 - Prob. 22E Ch. 7.3 - Prob. 23E Ch. 7.3 - Prob. 24E Ch. 7.3 - In Exercises 23-28, find a bound on the error in...Ch. 7.3 - Prob. 26E Ch. 7.3 - Prob. 27E Ch. 7.3 - Prob. 28E Ch. 7.3 - Prob. 29E Ch. 7.3 - Condominium Resort Complex Cooper Realty is...Ch. 7.3 - AVERAGE Temperature The graph depicted ill the...Ch. 7.3 - Surface area of the Jacqueline Kennedy Onassis...Ch. 7.3 - Fuel Consumption of Domestic Cars Thanks to...Ch. 7.3 - Prob. 34E Ch. 7.3 - Medical Costs for Veterans According to a study by...Ch. 7.3 - Prob. 36E Ch. 7.3 - Prob. 37E Ch. 7.3 - Consumers Surplus Refer to Section 6.7. 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The...Ch. 7.5 - The Fountains OF Bellagio Refer to Example 4. The...Ch. 7.5 - Prob. 52E Ch. 7.5 - Reaction Time Of A Motorist The amount of time (in...Ch. 7.5 - Prob. 54E Ch. 7.5 - Prob. 55E Ch. 7.5 - Prob. 56E Ch. 7.5 - Prob. 57E Ch. 7.5 - Prob. 59E Ch. 7.5 - Prob. 60E Ch. 7.5 - Prob. 61E Ch. 7.5 - Prob. 62E Ch. 7.5 - Prob. 63E Ch. 7.5 - Prob. 64E Ch. 7.5 - Prob. 65E Ch. 7.5 - Prob. 66E Ch. 7.5 - Prob. 67E Ch. 7.5 - Prob. 68E Ch. 7.5 - Prob. 69E Ch. 7.5 - Prob. 70E Ch. 7 - Fill in the blanks. 1. The integration by parts...Ch. 7 - Prob. 2CRQ Ch. 7 - Prob. 3CRQ Ch. 7 - Prob. 4CRQ Ch. 7 - Prob. 5CRQ Ch. 7 - Prob. 1RE Ch. 7 - Prob. 2RE Ch. 7 - Prob. 3RE Ch. 7 - Prob. 4RE Ch. 7 - Prob. 5RE Ch. 7 - Prob. 6RE Ch. 7 - Prob. 7RE Ch. 7 - Prob. 8RE Ch. 7 - Prob. 9RE Ch. 7 - Prob. 10RE Ch. 7 - Prob. 11RE Ch. 7 - Prob. 12RE Ch. 7 - Prob. 13RE Ch. 7 - Prob. 14RE Ch. 7 - Prob. 15RE Ch. 7 - Prob. 16RE Ch. 7 - Prob. 17RE Ch. 7 - Prob. 18RE Ch. 7 - Prob. 19RE Ch. 7 - Prob. 20RE Ch. 7 - Prob. 21RE Ch. 7 - Prob. 22RE Ch. 7 - Prob. 23RE Ch. 7 - Prob. 24RE Ch. 7 - Prob. 25RE Ch. 7 - Prob. 26RE Ch. 7 - Prob. 27RE Ch. 7 - Prob. 28RE Ch. 7 - Prob. 29RE Ch. 7 - Prob. 30RE Ch. 7 - Prob. 31RE Ch. 7 - Prob. 32RE Ch. 7 - Prob. 33RE Ch. 7 - Prob. 34RE Ch. 7 - Prob. 35RE Ch. 7 - Prob. 36RE Ch. 7 - Prob. 37RE Ch. 7 - Oil Spills Using aerial photographs, the Coast...Ch. 7 - Surface area OF a Lake a man-made lake located in...Ch. 7 - Prob. 40RE Ch. 7 - Prob. 1BM Ch. 7 - Prob. 2BM Ch. 7 - Prob. 3BM Ch. 7 - Prob. 4BM Ch. 7 - Prob. 5BM Ch. 7 - Prob. 6BM

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The function f ( x ) = 1 9 ( x 9 − x 2 ) is a probability density function on the interval [ 0 , 3 ] .

Solution Summary: The author explains that the function f(x) is a probability density function if it satisfies the above two properties.

To show: The function f(x)=19(x9−x2) is a probability density function on the interval [0,3] .

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Chapter 7 Solutions