Explanation Given: The mean of exponential distribution is 10 years. The amount to be paid if the equipment fails during first year is x . The amount to be paid if the equipment fails during second or third year is 0.5 x . No payment will be made if the equipment fails after 3 years. That is, payment = { x for 0 ≤ x ≤ 1 0.5 x for 1 ≤ x ≤ 3 0 for x > 3 Definition used: 1. Exponential Distribution: If X is a random variable with probability density function f ( x ) = a e − a x for x in [ 0 , ∞ ) . Then μ = 1 a . 2. Probability density function on ( − ∞ , ∞ ) . If f is a probability density function for a random variable X in the interval ( − ∞ , ∞ ) then, 1. P ( X ≤ b ) = P ( X < b ) = ∫ − ∞ b f ( x ) d x 2. P ( X ≥ a ) = P ( X > a ) = ∫ a ∞ f ( x ) d x 3. P ( − ∞ < X < ∞ ) = ∫ − ∞ ∞ f ( x ) d x = 1 Calculation: The probability density function is f ( x ) = a e − a x for x in [ 0 , ∞ ) . The mean of the distribution is 10 years. Consider the expected payment as follows, E ( X ) = 10 1 a = 10 a = 1 10 The exponential distribution f ( x ) = a e − a x can be written as f ( x ) = 1 10 e − 1 10 x for x in [ 0 , ∞ ) . Let the random variable be X

Finite Mathematics and Calculus with Applications

1st Edition

ISBN: 9781323188361

Author: Margaret Lial

Publisher: Pearson Education

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Chapter 18, Problem 51RE

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Chapter 18, Problem 50RE

Chapter 18, Problem 52RE

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u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (ū+v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅w) Support your answer mathematically or a with a written explanation. d) If possible, find u. (vxw) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Question 3 (6 points) u, v and w are three coplanar vectors: ⚫ w has a magnitude of 10 and points along the positive x-axis ⚫ v has a magnitude of 3 and makes an angle of 58 degrees to the positive x- axis ⚫ u has a magnitude of 5 and makes an angle of 119 degrees to the positive x- axis ⚫ vector v is located in between u and w a) Draw a diagram of the three vectors placed tail-to-tail at the origin of an x-y plane. b) If possible, find w × (u + v) Support your answer mathematically or a with a written explanation. c) If possible, find v. (ū⋅ w) Support your answer mathematically or a with a written explanation. d) If possible, find u (v × w) Support your answer mathematically or a with a written explanation. Note: in this question you can work with the vectors in geometric form or convert them to algebraic vectors.

Chapter 18 Solutions

Finite Mathematics and Calculus with Applications

Ch. 18.1 - Prob. 1YT Ch. 18.1 - Prob. 2YT Ch. 18.1 - Using the probability density function of Example...Ch. 18.1 - Use part (a) of Example 5 to calculate the...Ch. 18.1 - Evaluate each of the following integrals. (Sec....Ch. 18.1 - Prob. 2WE Ch. 18.1 - Prob. 3WE Ch. 18.1 - Decide whether the functions defined as follows...Ch. 18.1 - Prob. 2E Ch. 18.1 - Prob. 3E

Ch. 18.1 - Prob. 4E Ch. 18.1 - Prob. 5E Ch. 18.1 - Prob. 6E Ch. 18.1 - Prob. 7E Ch. 18.1 - Prob. 8E Ch. 18.1 - Prob. 9E Ch. 18.1 - Prob. 10E Ch. 18.1 - Prob. 11E Ch. 18.1 - Prob. 12E Ch. 18.1 - Prob. 13E Ch. 18.1 - Prob. 14E Ch. 18.1 - Prob. 15E Ch. 18.1 - Prob. 16E Ch. 18.1 - Prob. 17E Ch. 18.1 - Prob. 18E Ch. 18.1 - Prob. 19E Ch. 18.1 - Prob. 20E Ch. 18.1 - Prob. 21E Ch. 18.1 - Find the cumulative distribution function for the...Ch. 18.1 - Prob. 23E Ch. 18.1 - Prob. 24E Ch. 18.1 - Prob. 25E Ch. 18.1 - Prob. 26E Ch. 18.1 - Prob. 27E Ch. 18.1 - Prob. 28E Ch. 18.1 - Prob. 29E Ch. 18.1 - Prob. 30E Ch. 18.1 - Prob. 31E Ch. 18.1 - Prob. 32E Ch. 18.1 - Prob. 33E Ch. 18.1 - Prob. 34E Ch. 18.1 - Life Span of a Computer Part The life (in months)...Ch. 18.1 - Prob. 36E Ch. 18.1 - Prob. 37E Ch. 18.1 - Prob. 38E Ch. 18.1 - Prob. 39E Ch. 18.1 - Prob. 40E Ch. 18.1 - Prob. 41E Ch. 18.1 - Flea Beetles The mobility of an insect is an...Ch. 18.1 - Prob. 43E Ch. 18.1 - Prob. 44E Ch. 18.1 - Prob. 45E Ch. 18.1 - Earthquakes The time between major earthquakes in...Ch. 18.1 - Earthquakes The time between major earthquakes in...Ch. 18.1 - Prob. 48E Ch. 18.1 - Driving Fatalities We saw in a review exercise in...Ch. 18.1 - Prob. 50E Ch. 18.1 - Time of Traffic Fatality The National Highway...Ch. 18.2 - Repeat Example l for the probability density...Ch. 18.2 - Prob. 2YT Ch. 18.2 - Prob. 3YT Ch. 18.2 - Find P(1 X 2) for each probability function on...Ch. 18.2 - Prob. 2WE Ch. 18.2 - Prob. 1E Ch. 18.2 - Prob. 2E Ch. 18.2 - Prob. 3E Ch. 18.2 - Prob. 4E Ch. 18.2 - Prob. 5E Ch. 18.2 - Prob. 6E Ch. 18.2 - Prob. 7E Ch. 18.2 - In Exercises 18, a probability density function of...Ch. 18.2 - Prob. 9E Ch. 18.2 - Prob. 10E Ch. 18.2 - Prob. 11E Ch. 18.2 - Prob. 12E Ch. 18.2 - Prob. 13E Ch. 18.2 - Prob. 14E Ch. 18.2 - Prob. 15E Ch. 18.2 - Prob. 16E Ch. 18.2 - Prob. 17E Ch. 18.2 - For Exercises 1520, (a) find the median of the...Ch. 18.2 - Prob. 19E Ch. 18.2 - Prob. 20E Ch. 18.2 - Prob. 21E Ch. 18.2 - Prob. 22E Ch. 18.2 - Prob. 23E Ch. 18.2 - Prob. 24E Ch. 18.2 - Prob. 25E Ch. 18.2 - Prob. 26E Ch. 18.2 - Losses After Deductible A manufacturers annual...Ch. 18.2 - Prob. 28E Ch. 18.2 - Prob. 29E Ch. 18.2 - Prob. 30E Ch. 18.2 - Prob. 31E Ch. 18.2 - Prob. 32E Ch. 18.2 - Petal Length The length (in centimeters) of a...Ch. 18.2 - Prob. 34E Ch. 18.2 - Prob. 35E Ch. 18.2 - Prob. 36E Ch. 18.2 - Prob. 37E Ch. 18.2 - Prob. 38E Ch. 18.2 - Annual Rainfall The annual rainfall in a remote...Ch. 18.2 - Prob. 40E Ch. 18.2 - Prob. 41E Ch. 18.2 - Prob. 42E Ch. 18.2 - Time of Traffic Fatality In Exercise 51 of the...Ch. 18.3 - Prob. 1YT Ch. 18.3 - Prob. 2YT Ch. 18.3 - Prob. 3YT Ch. 18.3 - Prob. 1WE Ch. 18.3 - Prob. 2WE Ch. 18.3 - Prob. 1E Ch. 18.3 - Prob. 2E Ch. 18.3 - Find (a) the mean of the distribution, (b) the...Ch. 18.3 - Prob. 4E Ch. 18.3 - Prob. 5E Ch. 18.3 - Prob. 6E Ch. 18.3 - Prob. 7E Ch. 18.3 - Prob. 8E Ch. 18.3 - Prob. 9E Ch. 18.3 - Prob. 10E Ch. 18.3 - Prob. 11E Ch. 18.3 - Prob. 12E Ch. 18.3 - Prob. 13E Ch. 18.3 - Prob. 14E Ch. 18.3 - Prob. 15E Ch. 18.3 - Prob. 16E Ch. 18.3 - Prob. 17E Ch. 18.3 - Prob. 18E Ch. 18.3 - Prob. 19E Ch. 18.3 - Prob. 20E Ch. 18.3 - Prob. 21E Ch. 18.3 - Prob. 22E Ch. 18.3 - Prob. 23E Ch. 18.3 - Prob. 24E Ch. 18.3 - Prob. 25E Ch. 18.3 - Prob. 26E Ch. 18.3 - Prob. 27E Ch. 18.3 - Prob. 28E Ch. 18.3 - Prob. 29E Ch. 18.3 - Prob. 30E Ch. 18.3 - Prob. 31E Ch. 18.3 - Prob. 32E Ch. 18.3 - Prob. 33E Ch. 18.3 - Prob. 34E Ch. 18.3 - Insured Loss An insurance policy is written to...Ch. 18.3 - Prob. 36E Ch. 18.3 - Printer Failure The lifetime of a printer costing...Ch. 18.3 - Prob. 38E Ch. 18.3 - Prob. 39E Ch. 18.3 - Prob. 40E Ch. 18.3 - Prob. 41E Ch. 18.3 - Prob. 42E Ch. 18.3 - Finding Prey H. 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Pulliam found that the time (in...Ch. 18.3 - Life Expectancy According to the National Center...Ch. 18.3 - Prob. 45E Ch. 18.3 - Prob. 46E Ch. 18.3 - Prob. 47E Ch. 18.3 - Prob. 48E Ch. 18.3 - Prob. 49E Ch. 18.3 - Prob. 50E Ch. 18.3 - Prob. 51E Ch. 18.3 - Prob. 52E Ch. 18.3 - Prob. 53E Ch. 18.3 - Prob. 54E Ch. 18 - Prob. 1RE Ch. 18 - Prob. 2RE Ch. 18 - Prob. 3RE Ch. 18 - Prob. 4RE Ch. 18 - Prob. 5RE Ch. 18 - Prob. 6RE Ch. 18 - Prob. 7RE Ch. 18 - Prob. 8RE Ch. 18 - Prob. 9RE Ch. 18 - Prob. 10RE Ch. 18 - Prob. 11RE Ch. 18 - Prob. 12RE Ch. 18 - Prob. 13RE Ch. 18 - Prob. 14RE Ch. 18 - Prob. 15RE Ch. 18 - Prob. 16RE Ch. 18 - Prob. 17RE Ch. 18 - Prob. 18RE Ch. 18 - Prob. 19RE Ch. 18 - Prob. 20RE Ch. 18 - Prob. 21RE Ch. 18 - Prob. 22RE Ch. 18 - Prob. 23RE Ch. 18 - Prob. 24RE Ch. 18 - Prob. 25RE Ch. 18 - Prob. 26RE Ch. 18 - Prob. 27RE Ch. 18 - Prob. 28RE Ch. 18 - Prob. 29RE Ch. 18 - Prob. 30RE Ch. 18 - Prob. 31RE Ch. 18 - Prob. 32RE Ch. 18 - Prob. 33RE Ch. 18 - Prob. 34RE Ch. 18 - Prob. 35RE Ch. 18 - Prob. 36RE Ch. 18 - Prob. 37RE Ch. 18 - Prob. 38RE Ch. 18 - Prob. 39RE Ch. 18 - Prob. 40RE Ch. 18 - Prob. 41RE Ch. 18 - Prob. 42RE Ch. 18 - Prob. 43RE Ch. 18 - Prob. 44RE Ch. 18 - Prob. 45RE Ch. 18 - Prob. 46RE Ch. 18 - Prob. 47RE Ch. 18 - Prob. 48RE Ch. 18 - Prob. 49RE Ch. 18 - Prob. 50RE Ch. 18 - Prob. 51RE Ch. 18 - Prob. 52RE Ch. 18 - Prob. 53RE Ch. 18 - Prob. 54RE Ch. 18 - Prob. 55RE Ch. 18 - Prob. 56RE Ch. 18 - Prob. 57RE Ch. 18 - Prob. 58RE Ch. 18 - Prob. 59RE Ch. 18 - Prob. 60RE Ch. 18 - Prob. 61RE Ch. 18 - Prob. 62RE

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The level x of set for which the expected payment made under this insurance is to be 1000 and choose the correct answer.

Solution Summary: The author explains that if x is a random variable with probability density function f(x)=ae-ax, no payment will be made after 3 years.

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To find: The level x of set for which the expected payment made under this insurance is to be 1000 and choose the correct answer.

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Chapter 18 Solutions