Explanation Given: The expression is ∫ b a f ( x ) d x = 1 . Calculation: The probability density function of random variable X in an interval I can be defined as follows: The total area of the graph of the function f is equal to 1. The probability of the random variable X lies in the interval [ a , b ] can be calculated as follows: P ( a ≤ X ≤ b ) = ∫ a b f ( x ) d x Here, the function f ( x ) is the non-negative function. If the total area of the function on an interval is equal to 1 then the function is probability density function. In the statement the area of the function is equal to 1 on an interval [ a , b ]

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Question

Chapter 10.1, Problem 63E

To determine

Whether the statement “If ∫baf(x)dx=1 then f(x) is a probability density function on [a,b]” is true or false.

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Chapter 10.1, Problem 62E

Chapter 10.1, Problem 64E

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Let X be the number of years before a particular type of machines will need replacement. Assume that X has the probability function f(1) = 0.1, f(2) = 0.2, f(3) = 0.2, f(4) = 0.2, f(5) = 0.3. Find the probability that the machine needs no replacement during the first 3 years.

Prove the theorem

Chapter 10 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 10.1 - Define the following terms in your own words: a....Ch. 10.1 - Prob. 2CQ Ch. 10.1 - Prob. 3CQ Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E

Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E Ch. 10.1 - Prob. 11E Ch. 10.1 - Prob. 12E Ch. 10.1 - Prob. 13E Ch. 10.1 - Prob. 14E Ch. 10.1 - Prob. 15E Ch. 10.1 - Prob. 16E Ch. 10.1 - Prob. 17E Ch. 10.1 - Prob. 18E Ch. 10.1 - Prob. 19E Ch. 10.1 - Prob. 20E Ch. 10.1 - Prob. 21E Ch. 10.1 - Prob. 22E Ch. 10.1 - Prob. 23E Ch. 10.1 - Prob. 24E Ch. 10.1 - Prob. 25E Ch. 10.1 - Prob. 26E Ch. 10.1 - Prob. 27E Ch. 10.1 - Prob. 28E Ch. 10.1 - Prob. 29E Ch. 10.1 - Prob. 30E Ch. 10.1 - Prob. 31E Ch. 10.1 - Prob. 32E Ch. 10.1 - Prob. 33E Ch. 10.1 - Prob. 34E Ch. 10.1 - Prob. 35E Ch. 10.1 - Prob. 36E Ch. 10.1 - Prob. 37E Ch. 10.1 - Prob. 38E Ch. 10.1 - Prob. 39E Ch. 10.1 - Prob. 40E Ch. 10.1 - Prob. 41E Ch. 10.1 - Prob. 42E Ch. 10.1 - Prob. 43E Ch. 10.1 - FREQUENCY OF ROAD REPAIRS The fraction of streets...Ch. 10.1 - Prob. 45E Ch. 10.1 - Prob. 46E Ch. 10.1 - Prob. 47E Ch. 10.1 - RELIABILITY OF MICROPROCESSORS The microprocessors...Ch. 10.1 - Prob. 49E Ch. 10.1 - Prob. 50E Ch. 10.1 - Prob. 51E Ch. 10.1 - Prob. 52E Ch. 10.1 - Prob. 53E Ch. 10.1 - Prob. 54E Ch. 10.1 - Prob. 55E Ch. 10.1 - Prob. 57E Ch. 10.1 - Prob. 58E Ch. 10.1 - PRODUCT RELIABILITY Hal has a tablet PC and a...Ch. 10.1 - Prob. 60E Ch. 10.1 - Prob. 61E Ch. 10.1 - Prob. 62E Ch. 10.1 - Prob. 63E Ch. 10.1 - Prob. 64E Ch. 10.1 - Prob. 65E Ch. 10.1 - Prob. 66E Ch. 10.1 - Prob. 1TE Ch. 10.1 - Prob. 2TE Ch. 10.1 - Prob. 3TE Ch. 10.1 - Prob. 4TE Ch. 10.2 - Prob. 1CQ Ch. 10.2 - Prob. 2CQ Ch. 10.2 - Prob. 3CQ Ch. 10.2 - In Exercises 114, find the mean, variance, and...Ch. 10.2 - Prob. 2E Ch. 10.2 - Prob. 3E Ch. 10.2 - Prob. 4E Ch. 10.2 - Prob. 5E Ch. 10.2 - Prob. 6E Ch. 10.2 - Prob. 7E Ch. 10.2 - Prob. 8E Ch. 10.2 - Prob. 9E Ch. 10.2 - Prob. 10E Ch. 10.2 - Prob. 11E Ch. 10.2 - Prob. 12E Ch. 10.2 - Prob. 13E Ch. 10.2 - Prob. 14E Ch. 10.2 - Prob. 15E Ch. 10.2 - PROBABILITY OF RAINFALL The amount of rainfall (in...Ch. 10.2 - Prob. 17E Ch. 10.2 - Prob. 18E Ch. 10.2 - Prob. 19E Ch. 10.2 - Prob. 20E Ch. 10.2 - Prob. 21E Ch. 10.2 - Prob. 22E Ch. 10.2 - Prob. 23E Ch. 10.2 - Prob. 24E Ch. 10.2 - Prob. 25E Ch. 10.2 - Prob. 26E Ch. 10.2 - Prob. 27E Ch. 10.2 - Prob. 28E Ch. 10.2 - Prob. 29E Ch. 10.2 - Prob. 30E Ch. 10.2 - Prob. 31E Ch. 10.2 - Prob. 32E Ch. 10.2 - Prob. 33E Ch. 10.2 - Prob. 34E Ch. 10.2 - Prob. 35E Ch. 10.2 - Prob. 36E Ch. 10.2 - Prob. 1TE Ch. 10.2 - Prob. 2TE Ch. 10.2 - Prob. 3TE Ch. 10.2 - Prob. 4TE Ch. 10.2 - Prob. 5TE Ch. 10.2 - Prob. 6TE Ch. 10.3 - Prob. 1CQ Ch. 10.3 - Prob. 2CQ Ch. 10.3 - Prob. 1E Ch. 10.3 - Prob. 2E Ch. 10.3 - Prob. 3E Ch. 10.3 - Prob. 4E Ch. 10.3 - Prob. 5E Ch. 10.3 - Prob. 6E Ch. 10.3 - Prob. 7E Ch. 10.3 - Prob. 8E Ch. 10.3 - Prob. 9E Ch. 10.3 - Prob. 10E Ch. 10.3 - Prob. 11E Ch. 10.3 - Prob. 12E Ch. 10.3 - Prob. 13E Ch. 10.3 - Prob. 14E Ch. 10.3 - Prob. 15E Ch. 10.3 - Prob. 16E Ch. 10.3 - Prob. 17E Ch. 10.3 - Prob. 18E Ch. 10.3 - Prob. 19E Ch. 10.3 - Prob. 20E Ch. 10.3 - Prob. 21E Ch. 10.3 - FACTORY WORKERS WAGES According to the data...Ch. 10.3 - Prob. 23E Ch. 10.3 - Bottling Jam The weights of jam bottled by Snyder ...Ch. 10.3 - Prob. 25E Ch. 10.3 - Prob. 26E Ch. 10.3 - Prob. 27E Ch. 10.3 - Prob. 28E Ch. 10.3 - Prob. 29E Ch. 10.3 - Prob. 30E Ch. 10.3 - Prob. 31E Ch. 10.3 - Prob. 32E Ch. 10.3 - Prob. 33E Ch. 10.3 - Prob. 34E Ch. 10 - Fill in the blanks. a. An activity with observable...Ch. 10 - Prob. 2CRQ Ch. 10 - Prob. 3CRQ Ch. 10 - Prob. 4CRQ Ch. 10 - Prob. 5CRQ Ch. 10 - Prob. 6CRQ Ch. 10 - Prob. 7CRQ Ch. 10 - Prob. 8CRQ Ch. 10 - Prob. 1RE Ch. 10 - Prob. 2RE Ch. 10 - Prob. 3RE Ch. 10 - Prob. 4RE Ch. 10 - Prob. 5RE Ch. 10 - Prob. 6RE Ch. 10 - Prob. 7RE Ch. 10 - Prob. 8RE Ch. 10 - Prob. 9RE Ch. 10 - Prob. 10RE Ch. 10 - Prob. 11RE Ch. 10 - Prob. 12RE Ch. 10 - Prob. 13RE Ch. 10 - Prob. 14RE Ch. 10 - Prob. 15RE Ch. 10 - Prob. 16RE Ch. 10 - Prob. 17RE Ch. 10 - Prob. 18RE Ch. 10 - Prob. 19RE Ch. 10 - Prob. 20RE Ch. 10 - Prob. 21RE Ch. 10 - Prob. 22RE Ch. 10 - Prob. 23RE Ch. 10 - Prob. 24RE Ch. 10 - Prob. 25RE Ch. 10 - Prob. 26RE Ch. 10 - Prob. 27RE Ch. 10 - Prob. 28RE Ch. 10 - Prob. 29RE Ch. 10 - Prob. 30RE Ch. 10 - Prob. 1BM Ch. 10 - Prob. 2BM Ch. 10 - Prob. 3BM Ch. 10 - Prob. 4BM

Knowledge Booster

Whether the statement “If ∫ b a f ( x ) d x = 1 then f ( x ) is a probability density function on [ a , b ] ” is true or false.

Whether the statement “If ∫baf(x)dx=1 then f(x) is a probability density function on [a,b]” is true or false.

Want to see the full answer?

Chapter 10 Solutions