2.2.6A car panel is spray-painted by a machine, and the technicians are particularly interested in the thickness of the resulting paint layer. Suppose that the random variable X measures the thickness of the paint in millimeters at a randomly chosen point on a randomly chosen car panel, and that X takes values between 0.125 and 0.5 mm with a probability density function of f(x) = A(0.5 - (x - 0.25)²) for 0.125 ≤x≤ 0.5 and f(x) = 0 elsewhere. (a) Find the value of A and sketch the probability density function. (b) Construct and sketch the cumulative distribution function. (c) What is the probability that the paint thickness at a particular point is less than 0.2 mm?
2.2.6A car panel is spray-painted by a machine, and the technicians are particularly interested in the thickness of the resulting paint layer. Suppose that the random variable X measures the thickness of the paint in millimeters at a randomly chosen point on a randomly chosen car panel, and that X takes values between 0.125 and 0.5 mm with a probability density function of f(x) = A(0.5 - (x - 0.25)²) for 0.125 ≤x≤ 0.5 and f(x) = 0 elsewhere. (a) Find the value of A and sketch the probability density function. (b) Construct and sketch the cumulative distribution function. (c) What is the probability that the paint thickness at a particular point is less than 0.2 mm?
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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Transcribed Image Text:2.2.6A car panel is spray-painted by a machine, and the technicians are particularly interested
in the thickness of the resulting paint layer. Suppose that the random variable X measures
the thickness of the paint in millimeters at a randomly chosen point on a randomly chosen
car panel, and that X takes values between 0.125 and 0.5 mm with a probability density
function of
f(x) = A(0.5 - (x - 0.25)²)
for 0.125 ≤x≤ 0.5 and f(x) = 0 elsewhere.
(a) Find the value of A and sketch the probability density function.
(b) Construct and sketch the cumulative distribution function.
(c) What is the probability that the paint thickness at a particular point is less than 0.2 mm?
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