A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is as shown below. Complete parts (a) through (c). 2 (7x 2y), 0sx1,0sys1 9 f(x,y) elsewhere 0 (a) Find the marginal density of X.

MATH351, Lecture MATH101 Lechung MATH381_Sheets .. 1 4 2 13 146% = 9. A fast-food restaurant operates both a drive through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is f (x, y) = Osxsl, Osys1 3 (x + 2y) 0 elsewhere a. Find the marginal density of X. b. Find the marginal density of Y. c. Find the probability that the drive-through facility is busy less than one-half of the time. 1 381, Sheet02, Spring 17/18 Page o searchA fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X and Y, respectively, be the proportions of the time that the drive-through and walk-in facilities are in use, and suppose that the joint density function of these random variables is as shown below. Complete parts (a) through (c). f(X,y) = 6/ N -(7x + 2y), Ox=1, 0sys1 elsewhere (a) Find the marginal density of X