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 pair 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
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 pair 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
A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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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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Please do part c
![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?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb5797eb8-13e9-4394-9d7f-9d6d1c519849%2F1feffbb1-3e77-4997-b386-3f2639335b9b%2Frth3kj_processed.jpeg&w=3840&q=75)
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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