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 0.01 2 0.03 3 0.07 4 0.01 0.03 0.01 1 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.02 0.01 0.07 0.06 0.01 0.03 0.01 3. 0.10 0.03 0.01 0.01 4 (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.
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 0.01 2 0.03 3 0.07 4 0.01 0.03 0.01 1 0.05 0.08 0.03 0.02 2 0.03 0.11 0.15 0.01 0.02 0.01 0.07 0.06 0.01 0.03 0.01 3. 0.10 0.03 0.01 0.01 4 (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.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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Problem 1P
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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
0.05
0.03
0.08
0.07
0.01
1
0.03
0.03
0.02
2
0.03
0.02
0.11
0.07
0.06
0.15
0.01
0.01
0.10
0.03
0.03
0.01
0.01
0.01
4
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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