Q2)A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomlyselected day, let X and Y, respectively, be the propor-tions of the time that the drive-through and walk-infacilities are in use, and suppose that the joint densityfunction of these random variables isf(x, y)=[(x+2y),10,0≤x≤ 1,0 ≤ y ≤ 1,elsewhere.(a) Find the marginal density of X.(b) Find the marginal density of Y.(c) Find the probability that the drive-through facilityis busy less than one-half of the time.

Let X and Y be two continuous random variables defined over the sample space S. Then the continuous…

Answered: A fast-food restaurant operates both a…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 32E

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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(z,y) = { K (2³² + (x² + y²) 20 ≤ ≤ 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? Oves, f(x, y) = fx(z) - fy (y), so X and Y are independent. Oves, f(z,y) #fx(z) - 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(z) - fy(u), so X and Y are not independent.

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