2.2.6A car panel is spray-painted by a machine, and the technicians are particularly interestedin the thickness of the resulting paint layer. Suppose that the random variable X measuresthe thickness of the paint in millimeters at a randomly chosen point on a randomly chosencar panel, and that X takes values between 0.125 and 0.5 mm with a probability densityfunction off(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?

Answered: Image /qna-images/answer/800b7483-7f93-4b66-bc54-fea47a5c3394.jpg

Answered: 2.2.6A car panel is spray-painted by a…

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...

See similar textbooks

Similar questions

5. Suppose that X is a discrete random variable with probability density function x = 1, 2, 3, 4. p(x) = cx², (a) Find the value of c. Select one: О а. 1/25 O b. 1/30 О с. 30 O d. none
Suppose a random variable has a continuous uniform distribution between 0 and 10, such that its probability density function is: f(x) = 1/10. a. What is the cumulative density function for x? b. What is the mean (expected value) of x? c. What is the variance of x? d. According to Chebychef's rule, what is the smallest probability a random x will within 2 standard deviations of its mean? i.e. P(x-μ<2*o) e. What is the exact probability that a random x will fall within 2 standard deviations of its mean for this uniform distribution?
6.74 Let Y₁, ₂, ..., Y, be independent, uniformly distributed random variables on the interval [0, 0]. Find the a probability distribution function of Y() = max(Y₁; Y₂;; Y₁). b density function of y(n). c mean and variance of y(n).
QI. The probability mass function of a random variable X is given by p(i) = ca' /i!, i = 0,1,2,..., where à is some positive value. Find (a) P{X = 0} and (b) P{X > 2}. %3D
Previously, De Anza's statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of $0.88. Suppose that we randomly pick 25 daytime statistics students. Find the probability that an individual had between $0.80 and $1.00. Graph the situation, and shade in the area to be determined.
Suppose X is a random variable defined as final cost of project estimated cost of project which has a PDF as follows: [0 xa a. Determine the value of a. b. What is the probability that the final cost of a project will exceed its estimated cost by 25%? c. Determine the mean value and standard deviation of X.
2.70 Let X and Y be random variables with joint density function (4xy, 0< x,y< 1, f(x,y)= {0, elsewhere. Find the expected value of Z = √X² + y².
DHL usually gives its customer a 60-minute window in which it expects home deliveries to be delivered. An independent consultant estimates that the final delivery time within the window is a delivery that follows the following condensation function:a. Draw the density function of the event. b. What is the expected value of the transaction? c. What is the variance of the event?
Let Y denote a random variable with the following cumulative distribution function. if y 1. F(y) : In(4) a. Find the PDF, ƒ(y). b. Evaluate P(Y = 0.5). c. Evaluate P(Y 0.4). d. Evaluate P(Y < 1).
A random variable, X, has a pdf given by The expected value of Y is O a. 3/5 O b. 5/3 O c. 7/5 O A random variable Y, is related to X by Px(x) d. 7/3 = 1 -3 < x < 1. and 0 otherwise 4 Y = X²
3.1 The proportion of time per day that all checkout counters in a Checkers Hypermarket are busy is a random variable Y with a density function given by Oy²(1 – y), 0 < y< 1 %3D 0, elsewhere Find the mean and standard deviation and interpret your answer.
1. The loss due to a fire in a commercial building is modelled by a random variable X with density function Let X be a random variable with probability distribution table given below 10 20 50 100 P(X=x) | 0.4 | 0.3 | 0.15 | 0.1 | 0.05 Prepare the cdf of X.

SEE MORE QUESTIONS

Recommended textbooks for you

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability (10th Edition)

Probability

ISBN:

9780134753119

Author:

Sheldon Ross

Publisher:

PEARSON

A First Course in Probability

Probability

ISBN:

9780321794772

Author:

Sheldon Ross

Publisher:

PEARSON

SEE MORE TEXTBOOKS