Consider a fast-food restaurant in Izmir that operates both a drive-through facility anda walk-in facility. Let X and Y be the proportions of the time that the drive-through and walk-in facilitios are in use, respectively. Suppose that the joint density function of these random variables is as shown below. Complote parts (a) through (c). 13 (8x + 5y), 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. h(y) = for 0sys1 O B. g(x) = for 0sxs1 (b) Find the marginal density of Y. 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 (c) Find the probability that the drive-through facility is busy less than one-quarter of the time. The probability is O (Type an integer or a simplified fraction.)
Consider a fast-food restaurant in Izmir that operates both a drive-through facility anda walk-in facility. Let X and Y be the proportions of the time that the drive-through and walk-in facilitios are in use, respectively. Suppose that the joint density function of these random variables is as shown below. Complote parts (a) through (c). 13 (8x + 5y), 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. h(y) = for 0sys1 O B. g(x) = for 0sxs1 (b) Find the marginal density of Y. 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 (c) Find the probability that the drive-through facility is busy less than one-quarter of the time. The probability is O (Type an integer or a simplified fraction.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Consider a fast-food restaurant in Izmir that operates both a drive-through facility and a walk-in facility. Let X and Y be the proportions of the time that the drive-through and walk-in facilities are in use, respectively. Suppose that the joint density function of
these random variables is as shown below. Complete parts (a) through (c).
2
f(x.y) = 13 8x+ 5y), Osxs1,0sys1
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. h(y) =, for 0sys1
O B. g(x) =
for 0sxs1
(b) Find the marginal density of Y.
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
(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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