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A quality index summarizes different features of a product by means of a score. Different experts may assign different quality scores depending on thei experience with the product. Let X be the quality index for a tablet. Suppose the respective probability density function is given as follows: cx (2-x) if 0≤x≤2 elsewhere. f(x) = {cx (2- (a) Determine e such that f(x) is a proper PDF. (b) Determine the cumulative distribution function. (c) Calculate the expectation and variance of X.

A quality index summarizes different features of a product by means of a score. Different experts may assign different quality scores depending on thei experience with the product. Let X be the quality index for a tablet. Suppose the respective probability density function is given as follows: cx (2-x) if 0≤x≤2 elsewhere. f(x) = {cx (2- (a) Determine e such that f(x) is a proper PDF. (b) Determine the cumulative distribution function. (c) Calculate the expectation and variance of X.

A First Course in Probability (10th Edition)
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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A quality index summarizes different features of a product by means of a score. Different experts may assign different quality scores depending on their experience with the product. Let X be the quality index for a tablet. Suppose the respective probability density function is given as follows: cx (2-x) if 0≤x≤2 elsewhere. f(x) = = {₁x2²; 0 (a) Determine e such that f(x) is a proper PDF. (b) Determine the cumulative distribution function. (c) Calculate the expectation and variance of X. (d) Use Tscheby schev's inequality to determine the probability that X does not deviate more than 0.5 from its expectation.
Transcribed Image Text:A quality index summarizes different features of a product by means of a score. Different experts may assign different quality scores depending on their experience with the product. Let X be the quality index for a tablet. Suppose the respective probability density function is given as follows: cx (2-x) if 0≤x≤2 elsewhere. f(x) = = {₁x2²; 0 (a) Determine e such that f(x) is a proper PDF. (b) Determine the cumulative distribution function. (c) Calculate the expectation and variance of X. (d) Use Tscheby schev's inequality to determine the probability that X does not deviate more than 0.5 from its expectation.
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