The time to repair a machine expressed in hour is a random variablewith distribution function given by:F(x)=0,x/2,1/2,x/4,1,ifx ≤ 0;if 0≤x≤ 1;if 1 ≤x≤ 2;if 2 ≤x≤ 4;if 4 ≤ x.a) Draw the distribution function.b) Compute the density function.c) If the repairing time is more than 1 hour, what is the probabilitythat it is greater than 3.5 hours?

The time to repair a machine expressed in hour is a random variable with distribution function :-

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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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1. Each rear tire on an experimental airplane is supposed to be lled to a pressure of 40 pounds per square inch (psi). Let Y1 denote the actual air pressure for the right tire and Y2 denote the actual air pressure for the left tire. Suppose that Y1 and Y2 are random variables with the joint density function attached as a photo. a) Find k. b) Find the joint distribution function for Y1 and Y2. c) Find the probability that both tires are underfilled.
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Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable, X for the right tire and Y for the left tire, with joint pdf f(x, y) = JK(r² + y²) 0 20≤x≤ 30, 20 ≤ y ≤ 30 otherwise (a) What is the value of K? (Enter your answer as a fraction.) K = (b) What is the probability that both tires are underfilled? (Round your answer to four decimal places.) (c) What is the probability that the difference in air pressure between the two tires is at most 2 psi? (Round your answer to four decimal places.) (d) Determine the (marginal) distribution of air pressure in the right tire alone. for 20≤x≤ 30 (e) Are X and Y independent rv's? OYes, f(x,y) = fx(z) - fy(y), so X and Y are independent. OYes, f(x, y) + fx(x) · fy(y), so X and Y are independent. ONO, f(x, y) = fx(z) fy(y), so X and Y are not independent. ONO, f(x, y) + fx(2) fy(y), so X and Y are not independent.

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