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.

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.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.1: Continuous Probability Models

Problem 35E

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