In England, a famous restaurant serves both a drive-through and a walk-in facilities. Assume X and Y be the proportions of the time that the drive-through and walk-in facilities are in use on a randomly selected day, respectively, and suppose that the joint density function of these random variables is as shown below. Complete parts (a) through (c). 2x + 3y), Osxs1,0sys1 f(x,y) = 0. elsewhere (a) Find the marginal density of X. Select the correct choice below and fill in the answer box to complete your choice. O A. g(x) =, for 0sxs1 O B. h(y) =, for Osys1 (b) Find the marginal density of Y. Select the correct choice below and fill in the answer box to complete your choice. O A. h(y) =, for Osys1 O B. 9(x) = , for Osxs1 (c) Find the probability that the drive-through facility is busy less than one-quarter of the time. The probability is (Type an integer or a simplified fraction.)

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In England, a famous restaurant serves both a drive-through and a walk-in facilities. Assume X and Y be the proportions of the time that the drive-through and walk-in facilities are in use on a randomly selected day, respectively, and suppose that the joint density function of these random
variables is as shown below. Complete parts (a) through (c).
2
5 (2x + 3y), OsxS1, 0sys1
f(x,y) =
0,
elsewhere
(a) Find the marginal density of X.
Select the correct choice below and fill in the answer box to complete your choice.
O A. g(x) =
for 0sxs1
O B. h(y) =
for 0sys1
(b) Find the marginal density of Y.
Select the correct choice below and fill in the answer box to complete your choice.
O A. h(y) =
for 0sy<1
O B. g(x) =
for 0sxs1
(c) Find the probability that the drive-through facility is busy less than one-quarter of the time.
The probability is
(Type an integer or a simplified fraction.)
Transcribed Image Text:In England, a famous restaurant serves both a drive-through and a walk-in facilities. Assume X and Y be the proportions of the time that the drive-through and walk-in facilities are in use on a randomly selected day, respectively, and suppose that the joint density function of these random variables is as shown below. Complete parts (a) through (c). 2 5 (2x + 3y), OsxS1, 0sys1 f(x,y) = 0, elsewhere (a) Find the marginal density of X. Select the correct choice below and fill in the answer box to complete your choice. O A. g(x) = for 0sxs1 O B. h(y) = for 0sys1 (b) Find the marginal density of Y. Select the correct choice below and fill in the answer box to complete your choice. O A. h(y) = for 0sy<1 O B. g(x) = for 0sxs1 (c) Find the probability that the drive-through facility is busy less than one-quarter of the time. The probability is (Type an integer or a simplified fraction.)
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