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 X2X11340.010.010.030.070.010.050.1110.030.080.030.0220.030.150.010.010.020.070.100.030.0140.010.060.030.010.01(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).Give the standard deviation of X1.

We want to find the marginal probability distribution of X1 , marginal probability distribution of…

X2 X1 1 3 4 0.01 0.01 0.03 0.07 0.01 0.05 0.11 1 0.03 0.08 0.03 0.02 2 0.03 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. lolo

X2 X1 1 3 4 0.01 0.01 0.03 0.07 0.01 0.05 0.11 1 0.03 0.08 0.03 0.02 2 0.03 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. lolo

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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
0.01
0.03
0.07
0.01
0.05
0.11
1
0.03
0.08
0.03
0.02
2
0.03
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).
Give the standard deviation of X1.

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