6. A fast-paced 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, S{(x + 2y) if 0

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6. A fast-paced 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(æ) = {3
(x+ 2y) if 0 < æ < 1,0 < y < 1
if elsewhere
(a) Find the marginal density of X, (b) find the
marginal density of Y, and (c) find the probability
that the drive-through facility is busy less than
one-half of the time.
Transcribed Image Text:6. A fast-paced 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(æ) = {3 (x+ 2y) if 0 < æ < 1,0 < y < 1 if elsewhere (a) Find the marginal density of X, (b) find the marginal density of Y, and (c) find the probability that the drive-through facility is busy less than one-half of the time.
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