2. A fast-food restaurant operates both a drive through facility and a walk-in facility. On a randomly selected day, let

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2 A Fast Food Restaurant Operates Both A Drive Through Facility And A Walk In Facility On A Randomly Selected Day Let 1 (40.66 KiB) Viewed 110 times

2. 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 2 f(x,y) = (x + 2y), 0 sxs 1,0 sy si (a) Find the marginal probability density function of X. (b) Find the marginal probability density function of Y. (c) Find the conditional probability density function of X. (d) Find the conditional probability density function of Y. (e) Are X and Y independent? (You need to explain.) (f) Find the probability that the drive-through facility is busy less than one-half of the time.