A 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 a) b) d) e) f(x)=A[0.5-(x-0.25)2] for 0.125≤x≤0.5 and f(x)=0 elsewhere. Find the value of A that make f(x) a valid pdf. Construct the cumulative distribution function. Find the probability that the paint thickness at particular point is less than 0.2 mm, larger than 0.35mm, and between 0.35 and 0.2 mm respectively. What is the expected paint thickness? What is the variance and standard deviation of paint thickness?
A 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 a) b) d) e) f(x)=A[0.5-(x-0.25)2] for 0.125≤x≤0.5 and f(x)=0 elsewhere. Find the value of A that make f(x) a valid pdf. Construct the cumulative distribution function. Find the probability that the paint thickness at particular point is less than 0.2 mm, larger than 0.35mm, and between 0.35 and 0.2 mm respectively. What is the expected paint thickness? What is the variance and standard deviation of paint thickness?
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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![Problem 1.
A 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
a)
b)
d)
f(x)=A[0.5-(x-0.25)2] for 0.125≤x≤0.5 and f(x)=0 elsewhere.
Find the value of A that make f(x) a valid pdf.
Construct the cumulative distribution function.
Find the probability that the paint thickness at particular point is less than 0.2 mm, larger than
0.35mm, and between 0.35 and 0.2 mm respectively.
What is the expected paint thickness?
What is the variance and standard deviation of paint thickness?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff76c8be9-837b-45c9-b684-4f707af36e90%2F279e1a59-77b7-4f75-9bdf-099dfa498c5c%2Fi9v8f64_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Problem 1.
A 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
a)
b)
d)
f(x)=A[0.5-(x-0.25)2] for 0.125≤x≤0.5 and f(x)=0 elsewhere.
Find the value of A that make f(x) a valid pdf.
Construct the cumulative distribution function.
Find the probability that the paint thickness at particular point is less than 0.2 mm, larger than
0.35mm, and between 0.35 and 0.2 mm respectively.
What is the expected paint thickness?
What is the variance and standard deviation of paint thickness?
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