(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). (e) Give E(X2).
(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). (e) Give E(X2).
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 11ECP: A manufacturer has determined that a machine averages one faulty unit for every 500 it produces....
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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 |
0 |
1 |
2 |
3 |
4 |
|
0 |
0.01 |
0.01 |
0.03 |
0.07 |
0.01 |
|
1 |
0.03 |
0.05 |
0.08 |
0.03 |
0.02 |
|
2 |
0.03 |
0.11 |
0.15 |
0.01 |
0.01 |
|
3 |
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).
(e) Give E(X2).
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