A quality index summarizes different features of a product by meansof a score. Different experts may assign different quality scores depending on theirexperience with the product. Let X be the quality index for a tablet. Suppose therespective probability density function is given as follows:cx (2-x) if 0≤x≤2elsewhere.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 notdeviate more than 0.5 from its expectation.

Given f(x)=cx(2-x) 0≤x≤2 Note: According to Bartleby guidelines expert solve only one question and…

Answered: A quality index summarizes different…

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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Similar questions

11. Suppose random variable X is distributed as normal with mean 2 and standard deviation 3 and random variable Y with mean 0 and standard deviation 4, what is the probability density function (pdf) of X + Y.
4. Let X be a random variable with cumulative distribution function given by: F(r) = 1 – e-Az. Find the probability density function and so the expected value of variable X.
If X = ln Y has a normal distribution with the mean μand the standard deviation σ, find the probability densityof Y which is said to have the log-normal distribution.
The level of nitrogen oxides (NOX) and nonmethane organic gas (NMOG) in the exhaust over the useful life (150,000150,000 miles of driving) of cars of a particular model varies Normally with mean 8080 mg/mi and standard deviation 66 mg/mi. A company has 1616 cars of this model in its fleet. Using Table A, find the level ?L such that the probability that the average NOX + NMOG level ?¯x¯ for the fleet greater than ?L is only 0.030.03 ? (Enter your answer rounded to three decimal places. If you are using CrunchIt, adjust the default precision under Preferences as necessary. See the instructional video on how to adjust precision settings.)
For the random variable X with the probability function below, answer the following questions. f(x)= { 3x^2 , 0<x<1 { 0, otherwise a. Find the cdf of X. b. Find the probability that X is less than 0.5. c. Find E(X).
Suppose Y - Uniform(01, 02) where the parameters and 02 take the values 1 and 5 respectively. Compute the probability P(Y < y) when y=4.71.
The probability function of a continuous random variable, X, is given by the equation: fx(x) = 0.0064x(25-x²) for 0 < X < 5 Draw plots of both the pdf and the cdf of X.
Find the mean and variance of X given the following probability density function:
Find the characteristic function of X² when X has the N(u, o²) distribution.
Please provide Handwritten answer Question: Find probability distribution function for when: 0 < X < 3 3 < X < 6 X < 0 or X> 0, f(x) = 0
A random variable has the following probability density function (pdf), f(x) = { 0(2x - 2²) 0≤x≤2 0 otherwise Determine E(3X + 4)..

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