Measurements of scientific systems are always subject to variation, some more than others. There are manystructures for measurement error, and statisticians spend a great deal of time modeling these errors. Suppose themeasurement error X of a certain physical quantity is decided by the density function given below. Complete parts (a)through (c)JK(2-x²), -15xs1elsewhere.f(x) =(a) Determine k that renders f(x) a valid density function.k=(Type an integer or a simplified fraction)(b) Find the probability that a random error in measurement is less than -3The probability is(Type an integer or decimal rounded to three decimal places as needed.)(c) For this particular measurement, it is undesirable if the magnitude of the error (ie, Ix) exceeds 0.9. What is theprobability this occurs?The probability is(TvDe an integer or decimal rounded to three decimal places as needed.)

Answered: Measurements of scientific systems are…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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3.30 Measurements of scientific systems are always subject to variation, some more than others. There are many structures for measurement error, and statis- ticians spend a great deal of time modeling these errors. Suppose the measurement error X of a certain physical quantity is decided by the density function [k(3-x²), f(x) = 10, (a) Determine k that renders f(x) a valid density func- tion. (b) Find the probability that a random error in mea- surement is less than 1/2. −1≤x≤1, elsewhere. (c) For this particular measurement, it is undesirable if the magnitude of the error (i.e., |x|) exceeds 0.8. What is the probability that this occurs?
I need help with this, do I have the right answers?
Variable density structures and components are very common in engineering. For example, one such component is a modern civil aircraft wing. Even if it might be made out of the same material from its connection to the aircraft body to its tip, it has to include several different sub-components at different positions inside its hollow profile. So, if you want to calculate the total mass of the wing approximately at early stages of a design, you can try to find a scalar function that represents this variability in density and then represent the mass as a surface or volume integral. Even in an early stage of design, even a minimalist, but realistic 3D example would have been difficult to solve in an exam situation. We will certainly handle a much simpler case here and it will be in 2D. This introduction was just to give you an insight on what you try to achieve in questions similar to the following. Let's assume that the areal density of our component increases along y-axis and there is no…
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Solve parts 4,5,6 Thank you

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