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?

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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...

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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
The Exponential pdf for continuous random variable Y takes the form y > 0 f(y) = for ß > 0. y < 0 Suppose that a new random variable X is defined by X = cY. If the parameter B takes the value 2.10, and c=1, compute the probability P(X < 1.4) Give your answer to three decimal places.
x is a gaussian random variable with a PDF as described above, where μ is the mean, σ is the standard deviation , and Fx(X) refers to the cumulative distribution function CDF. It is known that Fx(-0.7) = 0.500 and Fx(1.3)=0.841, what value of Xo do we find the probability Fx(Xo) = P(X<Xo) = 0.023 ?
Consider the following normal distribution: 1 f(x) = exp[=1/2(x– µ)²lo²] Show that f(x) is a continuous probability distribution, that is, show that f(x)dx = 1.
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.
1. Which of the following is FALSE for a continuous random variable X with pdf y = f(x)? %3D A. P(6 S XS 9) = P(6 < X< 9) B. P(6 s XS 9) = f(6)+f(7)+f(8)+f(9) %3D C. P(6 < XS9) = area under the curve y=f(x) between 6 and 9 D. P(X = 9) = 0
For the given probability density function, over the given interval, find the mean, the variance, and the standard deviation. 36) f(x)== // [12, 20] 36) B) μ = 16; o² = 5.33; o = 2.31 A) μ = 15.5; o2=5.20; o = 2.28 C) μ = 15; o2 = 5.34; o = 2.31 D) μ= 1.6; o2 = 5.24; o=2.29
5. Suppose that X is a discrete random variable with probability density function p(x) = cx², x = 1, 2, 3, 4. (c) Find Var(X). Select one: O a. 18.4 O b. 354 O c. none O d. 342.8
Prob.5 Find the mean, the median, and the mode of the random variable X with the following probability density functions: (a) Gaussian distribution with parameters μ and o². (b) Exponential distribution with parameter 1. (c) Beta distribution with a = 3 and b = 4. (d) Uniform distribution in the interval (a, b).
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.
QUESTION 4 The probability density function for the time taken to complete a 1-hour test (X) by students is given by a) b) c) Find the value of c. f(x) = {cx² + x ! ) 0≤x≤1 elsewhere Find the probability that a randomly selected student will finish in at least half an hour. Calculate the variance of X.

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