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 X1 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 3 4 0.01 0.03 0.07 0.03 0.01 0.02 0.01 1 0.03 0.05 0.08 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.01 0.07 0.10 0.03 0.01 0.06 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/Y1)
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 X1 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 3 4 0.01 0.03 0.07 0.03 0.01 0.02 0.01 1 0.03 0.05 0.08 2 0.03 0.11 0.15 0.01 0.01 3 0.02 0.01 0.07 0.10 0.03 0.01 0.06 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/Y1)
MATLAB: An Introduction with Applications
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Chapter1: Starting With Matlab
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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 X1 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
0.07
0.01
1
0.03
0.05
0.08
0.03
0.02
0.03
0.11
0.15
0.01
0.01
0.02
0.07
0.10
0.03
0.01
4
0.01
0.06
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 E(X1| X2=3).
(g) Give the standard deviation of X1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe174b0c-aff2-48e8-b0c3-e14c959a6d86%2Ff0583156-5e38-4e03-b124-64eac6982bc8%2F7tw57t_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 X1 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
0.07
0.01
1
0.03
0.05
0.08
0.03
0.02
0.03
0.11
0.15
0.01
0.01
0.02
0.07
0.10
0.03
0.01
4
0.01
0.06
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 E(X1| X2=3).
(g) Give the standard deviation of X1.
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