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). f(x,y)= OA. h(y) = B. g(x)= 2 11 0, (a) Find the marginal density of X. Select the correct choice below and fill in the answer box to complete your choice. A. h(y) = " -(5x+6y), 0≤x≤ 1, 0≤ y ≤ 1 for 0 ≤ y ≤ 1 10x + 6 11 (b) Find the marginal density of Y. Select the correct choice below and fill in the answer box to complete your choice. 5+12y 11 " elsewhere for 0≤x≤ 1 B. g(x)= for 0≤x≤ 1 for 0 ≤ y ≤1 (c) Find the probability that the drive-through facility is busy less than one-third of the time. The probability is (Type an integer or a simplified fraction.)
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). f(x,y)= OA. h(y) = B. g(x)= 2 11 0, (a) Find the marginal density of X. Select the correct choice below and fill in the answer box to complete your choice. A. h(y) = " -(5x+6y), 0≤x≤ 1, 0≤ y ≤ 1 for 0 ≤ y ≤ 1 10x + 6 11 (b) Find the marginal density of Y. Select the correct choice below and fill in the answer box to complete your choice. 5+12y 11 " elsewhere for 0≤x≤ 1 B. g(x)= for 0≤x≤ 1 for 0 ≤ y ≤1 (c) Find the probability that the drive-through facility is busy less than one-third of the time. The probability is (Type an integer or a simplified fraction.)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Question
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Transcribed Image Text:A coin is tossed twice. Let Z denote the number of heads on the first toss and W the
total number of heads on the 2 tosses. Suppose the coin is unbalanced and a head has
a 64% chance of occurring. Complete parts (a) through (d).
(a) Find the joint probability distribution of W and Z.
Select the correct choice below and fill in the answer boxes to complete your choice.
(Type integers or decimals. Do not round.)
A.
B.
Z
B.
Z
f(w,z)
0
f(w,z)
0
W
g(w)
2
W
g(w)
0
0.1296
0
0
W
1
0.2304
0.2304
(b) Find the marginal distribution of W.
Select the correct choice below and fill in the answer boxes to complete your choice.
(Type integers or decimals. Do not round.)
A.
0
1
1
W
1
2
0
.4096
2
2
Transcribed Image Text: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).
f(x,y)=
O A. h(y) =
B. g(x)=
(a) Find the marginal density of X.
Select the correct choice below and fill in the answer box to complete your choice.
2
11
A. h(y) =
B. g(x) =
"
(5x+6y), 0≤x≤ 1, 0≤ y ≤1
for 0 ≤ y ≤ 1
10x + 6
11
(b) Find the marginal density of Y.
Select the correct choice below and fill in the answer box to complete your choice.
1
5+12y
11
elsewhere
"
for 0 ≤ x ≤ 1
for 0 ≤ y ≤ 1
for 0≤x≤ 1
(c) Find the probability that the drive-through facility is busy less than one-third of the
time.
The probability is
(Type an integer or a simplified fraction.)
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