X2 X1 1 2 3 0.07 0.03 4 0.01 0.01 0.03 0.08 0.01 0.03 0.03 1 0.05 0.02 0.11 О.15 0.01 0.01 3. 0.02 0.07 0.06 0.10 0.03 0.01 4. 0.01 0.03 0.01 0.01 (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional density distribution of X1 given X2 = 3. (d) Give E(X1). (c) Give E(X2). (f) Give EÇX1| X2=3). (g) Give the standard deviation of X1.
X2 X1 1 2 3 0.07 0.03 4 0.01 0.01 0.03 0.08 0.01 0.03 0.03 1 0.05 0.02 0.11 О.15 0.01 0.01 3. 0.02 0.07 0.06 0.10 0.03 0.01 4. 0.01 0.03 0.01 0.01 (a) Give the marginal density of X1. (b) Give the marginal density of X2. (c) Give the conditional density distribution of X1 given X2 = 3. (d) Give E(X1). (c) Give E(X2). (f) Give EÇX1| X2=3). (g) Give the standard deviation of X1.
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![A delivery truck travels from point A to point B and back using the same route each day.
There are four traffic lights on the route. Let Xi denote the number of red lights the truck
encounters going from A to B and X2 denote the number encountered on the return trip.
Data collected over a long period suggest that the joint probability distribution for (X1,
X2) is given by
X2
X1
1
2
3
4.
0.01
0.01
0.03
0.08
0.07
0.03
0.01
1
0.02
0.03
0.03
0.05
2
0.11
О.15
0.01
0.01
0.07
0.06
0.01
3
4
0.02
0.10
0.03
0.01
0.03
0.01
0.01
(a) Give the marginal density of X1.
(b) Give the marginal density of X2.
(c) Give the conditional density distribution of Xı given X2 = 3.
(d) Give E(X1).
(c) Give E(X2).
(f) Give E(X1| X2=3).
(g) Give the standard deviation of X1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc198e786-a4ae-4f87-9203-fcd37aaf3d4d%2F4e4edb3b-910f-4640-be89-7b87aee53a6b%2Fmzjjc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:A delivery truck travels from point A to point B and back using the same route each day.
There are four traffic lights on the route. Let Xi denote the number of red lights the truck
encounters going from A to B and X2 denote the number encountered on the return trip.
Data collected over a long period suggest that the joint probability distribution for (X1,
X2) is given by
X2
X1
1
2
3
4.
0.01
0.01
0.03
0.08
0.07
0.03
0.01
1
0.02
0.03
0.03
0.05
2
0.11
О.15
0.01
0.01
0.07
0.06
0.01
3
4
0.02
0.10
0.03
0.01
0.03
0.01
0.01
(a) Give the marginal density of X1.
(b) Give the marginal density of X2.
(c) Give the conditional density distribution of Xı given X2 = 3.
(d) Give E(X1).
(c) Give E(X2).
(f) Give E(X1| X2=3).
(g) Give the standard deviation of X1.
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